Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 CS02 Computer Sc. and Information Technology Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
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GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
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GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array
declaration. The dimension of the array is at least one. For example,
int a[10][3];
The grammars use D as the start symbol, and use six terminal symbolsint;id[]num.
GrammarG1 GrammarG2
D!intL; D!intL;
L!id[E L!idE
E!num] E! E[num]
E!num][E E![num]
Which of the grammars correctly generate the declaration mentioned above?
(A) BothG1 andG2
(B) OnlyG1
(C) OnlyG2
(D) NeitherG1 norG2
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given
in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time ?rst.
Process Arrival Time Burst Time
P
1
0 10
P
2
3 6
P
3
7 1
P
4
8 3
The average turn around time of these processes is milliseconds.
CS(Set B) 14/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array
declaration. The dimension of the array is at least one. For example,
int a[10][3];
The grammars use D as the start symbol, and use six terminal symbolsint;id[]num.
GrammarG1 GrammarG2
D!intL; D!intL;
L!id[E L!idE
E!num] E! E[num]
E!num][E E![num]
Which of the grammars correctly generate the declaration mentioned above?
(A) BothG1 andG2
(B) OnlyG1
(C) OnlyG2
(D) NeitherG1 norG2
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given
in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time ?rst.
Process Arrival Time Burst Time
P
1
0 10
P
2
3 6
P
3
7 1
P
4
8 3
The average turn around time of these processes is milliseconds.
CS(Set B) 14/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.48 Consider the following two-process synchronization solution.
Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;
Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;
The shared variableturn is initialized to zero. Which one of the following isTRUE?
(A) This is a correct two-process synchronization solution.
(B) This solution violates mutual exclusion requirement.
(C) This solution violates progress requirement.
(D) This solution violates bounded wait requirement.
Q.49 Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S)
increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in
some order. The largest initial value of S for which at least one P(S) operation will remain
blocked is .
CS(Set B) 15/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array
declaration. The dimension of the array is at least one. For example,
int a[10][3];
The grammars use D as the start symbol, and use six terminal symbolsint;id[]num.
GrammarG1 GrammarG2
D!intL; D!intL;
L!id[E L!idE
E!num] E! E[num]
E!num][E E![num]
Which of the grammars correctly generate the declaration mentioned above?
(A) BothG1 andG2
(B) OnlyG1
(C) OnlyG2
(D) NeitherG1 norG2
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given
in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time ?rst.
Process Arrival Time Burst Time
P
1
0 10
P
2
3 6
P
3
7 1
P
4
8 3
The average turn around time of these processes is milliseconds.
CS(Set B) 14/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.48 Consider the following two-process synchronization solution.
Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;
Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;
The shared variableturn is initialized to zero. Which one of the following isTRUE?
(A) This is a correct two-process synchronization solution.
(B) This solution violates mutual exclusion requirement.
(C) This solution violates progress requirement.
(D) This solution violates bounded wait requirement.
Q.49 Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S)
increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in
some order. The largest initial value of S for which at least one P(S) operation will remain
blocked is .
CS(Set B) 15/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.50 A ?le system uses an in-memory cache to cache disk blocks. The miss rate of the cache is
shown in the ?gure. The latency to read a block from the cache is 1 ms and to read a block
from the disk is 10 ms. Assume that the cost of checking whether a block exists in the cache
is negligible. Available cache sizes are in multiples of 10 MB.
10 20 30 40 50
10
60 70 80 90
20
30
40
50
60
70
80
90
0
0
Miss rate (%)
Cache size (MB)
The smallest cache size required to ensure an average read latency of less than 6 ms is
MB.
Q.51 Consider the following database schedule with two transactions, T
1
and T
2
.
S= r
2
(X); r
1
(X); r
2
(Y); w
1
(X); r
1
(Y); w
2
(X); a
1
; a
2
where r
i
(Z) denotes a read operation by transaction T
i
on a variable Z, w
i
(Z) denotes a write
operation by T
i
on a variable Z and a
i
denotes an abort by transaction T
i
.
Which one of the following statements about the above schedule isTRUE?
(A) S is non-recoverable
(B) S is recoverable, but has a cascading abort
(C) S does not have a cascading abort
(D) S is strict
CS(Set B) 16/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array
declaration. The dimension of the array is at least one. For example,
int a[10][3];
The grammars use D as the start symbol, and use six terminal symbolsint;id[]num.
GrammarG1 GrammarG2
D!intL; D!intL;
L!id[E L!idE
E!num] E! E[num]
E!num][E E![num]
Which of the grammars correctly generate the declaration mentioned above?
(A) BothG1 andG2
(B) OnlyG1
(C) OnlyG2
(D) NeitherG1 norG2
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given
in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time ?rst.
Process Arrival Time Burst Time
P
1
0 10
P
2
3 6
P
3
7 1
P
4
8 3
The average turn around time of these processes is milliseconds.
CS(Set B) 14/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.48 Consider the following two-process synchronization solution.
Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;
Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;
The shared variableturn is initialized to zero. Which one of the following isTRUE?
(A) This is a correct two-process synchronization solution.
(B) This solution violates mutual exclusion requirement.
(C) This solution violates progress requirement.
(D) This solution violates bounded wait requirement.
Q.49 Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S)
increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in
some order. The largest initial value of S for which at least one P(S) operation will remain
blocked is .
CS(Set B) 15/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.50 A ?le system uses an in-memory cache to cache disk blocks. The miss rate of the cache is
shown in the ?gure. The latency to read a block from the cache is 1 ms and to read a block
from the disk is 10 ms. Assume that the cost of checking whether a block exists in the cache
is negligible. Available cache sizes are in multiples of 10 MB.
10 20 30 40 50
10
60 70 80 90
20
30
40
50
60
70
80
90
0
0
Miss rate (%)
Cache size (MB)
The smallest cache size required to ensure an average read latency of less than 6 ms is
MB.
Q.51 Consider the following database schedule with two transactions, T
1
and T
2
.
S= r
2
(X); r
1
(X); r
2
(Y); w
1
(X); r
1
(Y); w
2
(X); a
1
; a
2
where r
i
(Z) denotes a read operation by transaction T
i
on a variable Z, w
i
(Z) denotes a write
operation by T
i
on a variable Z and a
i
denotes an abort by transaction T
i
.
Which one of the following statements about the above schedule isTRUE?
(A) S is non-recoverable
(B) S is recoverable, but has a cascading abort
(C) S does not have a cascading abort
(D) S is strict
CS(Set B) 16/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.52 Consider the following database table named water_schemes :
water_schemes
scheme_no district_name capacity
1 Ajmer 20
1 Bikaner 10
2 Bikaner 10
3 Bikaner 20
1 Churu 10
2 Churu 20
1 Dungargarh 10
The number of tuples returned by the following SQL query is .
with total(name, capacity) as
select district_name, sum(capacity)
from water_schemes
groupby district_name
with total_avg(capacity) as
select avg(capacity)
from total
select name
from total, total_avg
where total.capacity total_avg.capacity
Q.53 A network has a data transmission bandwidth of 20 10
6
bits per second. It uses CSMA/CD
in the MAC layer. The maximum signal propagation time from one node to another node is
40 microseconds. The minimum size of a frame in the network is bytes.
CS(Set B) 17/18
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-6
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (?, ?) is 4. Find the value of
???? ???? + ???? ???? ???? ? ???? + ???? ? ????
(A) n
4
(B) 4
n
(C) 2
2n-1
(D) 4
n-1
Q. 6 ? Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook
?
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
or
?
accounts. The number of faculty members connected only through Facebook
?
accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set-6
2/3
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only
(B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
GATE 2016 General Aptitude - GA Set-6
3/3
Q.10
Choose the correct expression for f(x) given in the graph.
(A) ???? ( ???? ) = 1 ?| ???? ?1| (B) ???? ( ???? ) = 1+| ???? ?1|
(C) ???? ( ???? ) = 2 ?| ???? ?1| (D) ???? ( ???? ) = 2+| ???? ?1|
END OF THE QUESTION PAPER
x
f(x)
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P_ Q
(v):Q_ P
The number of expressions given above that are logically implied by P^(P) Q) is
.
Q.2 Let f(x) be a polynomial and g(x)= f
0
(x) be its derivative. If the degree of( f(x)+ f( x)) is
10, then the degree of(g(x) g( x)) is .
Q.3 The minimum number of colours that is suf?cient to vertex-colour any planar graph is
.
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m< n, then all such systems have a solution
II. If m> n, then none of these systems has a solution
III. If m= n, then there exists a system which has a solution
Which one of the following isCORRECT?
(A) I, II and III are true
(B) Only II and III are true
(C) Only III is true
(D) None of them is true
CS(Set B) 1/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability
of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it
is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more
than 100 hours is .
Q.6 Suppose that the eigenvalues of matrix A are 1;2;4. The determinant of (A
1
)
T
is
.
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are
integers represented in 2?s complement form. If the decimal value of A is one, the decimal
value of B that leads to the longest latency for the sum to stabilize is .
Q.8 Let, x
1
x
2
x
3
x
4
= 0 where x
1
, x
2
, x
3
, x
4
are Boolean variables, and is the XOR operator.
Which one of the following must always beTRUE?
(A) x
1
x
2
x
3
x
4
= 0
(B) x
1
x
3
+ x
2
= 0
(C) ? x
1
? x
3
= ? x
2
? x
4
(D) x
1
+ x
2
+ x
3
+ x
4
= 0
Q.9 Let X be the number of distinct 16-bit integers in 2?s complement representation. Let Y be the
number of distinct 16-bit integers in sign magnitude representation.
Then X Y is .
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction
word has an opcode, two register operands and an immediate operand. The number of bits
available for the immediate operand ?eld is .
CS(Set B) 2/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is
a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the
maximum possible value of n is .
Q.12 The value printed by the following program is .
void f(int* p, int m){
m = m + 5;
*p = *p + m;
return;
}
void main(){
int i=5, j=10;
f(&i, j);
printf("%d", i+j);
}
Q.13 Assume that the algorithms considered here sort the input sequences in ascending order. If the
input is already in ascending order, which of the following areTRUE?
I. Quicksort runs inQ(n
2
) time
II. Bubblesort runs inQ(n
2
) time
III. Mergesort runs inQ(n) time
IV . Insertion sort runs inQ(n) time
(A) I and II only
(B) I and III only
(C) II and IV only
(D) I and IV only
CS(Set B) 3/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm.
(B) Divide-and-Conquer paradigm.
(C) Dynamic Programming paradigm.
(D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided
to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on
which the operation is to be performed.
An algorithm performs the following operations on the list in this order:Q(N) delete, O(logN)
insert, O(logN) ?nd, and Q(N) decrease-key. What is the time complexity of all these
operations put together?
(A) O(log
2
N) (B) O(N) (C) O(N
2
) (D) Q(N
2
logN)
Q.16 The number of states in the minimum sized DFA that accepts the language de?ned by the
regular expression
(0+ 1)
(0+ 1)(0+ 1)
is .
Q.17 Language L
1
is de?ned by the grammar: S
1
! aS
1
bje
Language L
2
is de?ned by the grammar: S
2
! abS
2
je
Consider the following statements:
P: L
1
is regular
Q: L
2
is regular
Which one of the following isTRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false
CS(Set B) 4/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.18 Consider the following types of languages: L
1
: Regular, L
2
: Context-free, L
3
: Recursive,
L
4
: Recursively enumerable. Which of the following is/areTRUE?
I. L
3
[ L
4
is recursively enumerable
II. L
2
[ L
3
is recursive
III. L
1
\ L
2
is context-free
IV . L
1
[ L
2
is context-free
(A) I only
(B) I and III only
(C) I and IV only
(D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records
(A) P$ i, Q$ ii, R$ iv, S$ iii
(B) P$ iii, Q$ i, R$ ii, S$ iv
(C) P$ ii, Q$ iii, R$ i, S$ iv
(D) P$ iv, Q$ i, R$ ii, S$ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate
to increase even when the number of allocated frames increases?
(A) LRU (Least Recently Used)
(B) OPT (Optimal Page Replacement)
(C) MRU (Most Recently Used)
(D) FIFO (First In First Out)
CS(Set B) 5/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.21 B+ Trees are consideredBALANCED because
(A) the lengths of the paths from the root to all leaf nodes are all equal.
(B) the lengths of the paths from the root to all leaf nodes differ from each other by at
most 1.
(C) the number of children of any two non-leaf sibling nodes differ by at most 1.
(D) the number of records in any two leaf nodes differ by at most 1.
Q.22 Suppose a database schedule S involves transactions T
1
, :::, T
n
. Construct the precedence
graph of S with vertices representing the transactions and edges representing the con?icts. If
S is serializable, which one of the following orderings of the vertices of the precedence graph
is guaranteed to yield a serial schedule?
(A) Topological order
(B) Depth-?rst order
(C) Breadth-?rst order
(D) Ascending order of transaction indices
Q.23 Anarkali digitally signs a message and sends it to Salim. Veri?cation of the signature by Salim
requires
(A) Anarkali?s public key.
(B) Salim?s public key.
(C) Salim?s private key.
(D) Anarkali?s private key.
Q.24 In an Ethernet local area network, which one of the following statements isTRUE?
(A) A station stops to sense the channel once it starts transmitting a frame.
(B) The purpose of the jamming signal is to pad the frames that are smaller than the
minimum frame size.
(C) A station continues to transmit the packet even after the collision is detected.
(D) The exponential backoff mechanism reduces the probability of collision on
retransmissions.
CS(Set B) 6/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.25 Identify the correct sequence in which the following packets are transmitted on the network
by a host when a browser requests a webpage from a remote server, assuming that the host has
just been restarted.
(A) HTTP GET request, DNS query, TCP SYN
(B) DNS query, HTTP GET request, TCP SYN
(C) DNS query, TCP SYN, HTTP GET request
(D) TCP SYN, DNS query, HTTP GET request
Q.26-Q.55carrytwomarkseach.
Q.26 A binary relation R onNN is de?ned as follows: (a;b)R(c;d) if a c or b d. Consider
the following propositions:
P: R is re?exive
Q: R is transitive
Which one of the following statements isTRUE?
(A) Both P and Q are true.
(B) P is true and Q is false.
(C) P is false and Q is true.
(D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus isNOT valid?
(A) (8x p(x))8xq(x)))(9x:p(x)_8xq(x))
(B) (9x p(x)_9xq(x)))9x(p(x)_ q(x))
(C)9x(p(x)^ q(x)))(9x p(x)^9xq(x))
(D)8x(p(x)_ q(x)))(8x p(x)_8xq(x))
CS(Set B) 7/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of
9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following
statements:
I. Each compound in Un S reacts with an odd number of compounds.
II. At least one compound in Un S reacts with an odd number of compounds.
III. Each compound in Un S reacts with an even number of compounds.
Which one of the above statements isALWAYSTRUE?
(A) Only I
(B) Only II
(C) Only III
(D) None
Q.29 The value of the expression 13
99
(mod 17), in the range 0 to 16, is .
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units
U
F
and U
G
, respectively. Given two instances of U
F
and two instances of U
G
, it is required to
implement the computation F(G(X
i
)) for 1 i 10. Ignoring all other delays, the minimum
time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction
has ?ve distinct ?elds, namely, opcode, two source register identi?ers, one destination register
identi?er, and a twelve-bit immediate value. Each instruction must be stored in memory in
a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes)
consumed by the program text is .
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag ?eld in a 512
KB 8-way set associative cache is bits.
CS(Set B) 8/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.33 Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies t
1
,
t
2
, and t
3
such that t
1
= 3t
2
=4= 2t
3
. If the longest pipeline stage is split into two pipeline
stages of equal latency, the new frequency is GHz, ignoring delays in the pipeline
registers.
Q.34 A complete binary min-heap is made by including each integer in [1;1023] exactly once.
The depth of a node in the heap is the length of the path from the root of the heap to that
node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is
.
Q.35 The following function computesX
Y
for positive integersX andY.
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Which one of the following conditions isTRUE before every iteration of the loop?
(A) X
Y
=a
b
(B) (resa)
Y
=(resX)
b
(C) X
Y
=resa
b
(D) X
Y
=(resa)
b
CS(Set B) 9/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 Consider the followingNew-order strategy for traversing a binary tree:
Visit the root;
Visit the right subtree usingNew-order;
Visit the left subtree usingNew-order;
TheNew-order traversal of the expression tree corresponding to the reverse polish expression
3 4 * 5 - 2 ? 6 7 * 1 + - is given by:
(A) + - 1 6 7 * 2 ? 5 - 3 4 *
(B) - + 1 * 6 7 ? 2 - 5 * 3 4
(C) - + 1 * 7 6 ? 2 - 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * - ? -
Q.37 Consider the following program:
int f(int *p, int n)
{
if (n <= 1) return 0;
else return max(f(p+1,n-1),p[0]-p[1]);
}
int main()
{
int a[] = {3,5,2,6,4};
printf("%d", f(a,5));
}
Note: max(x,y) returns the maximum ofx andy.
The value printed by this program is .
Q.38 Let A
1
;A
2
;A
3
; and A
4
be four matrices of dimensions 10 5;5 20;20 10, and 10 5,
respectively. The minimum number of scalar multiplications required to ?nd the product
A
1
A
2
A
3
A
4
using the basic matrix multiplication method is .
CS(Set B) 10/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.39 The given diagram shows the ?owchart for a recursive function A(n). Assume that all
statements, except for the recursive calls, have O(1) time complexity. If the worst case time
complexity of this function is O(n
a
), then the least possible value (accurate up to two decimal
positions) ofa is .
Start
A(n=2)
A(n=2) Return A(n=2) A(n=2) Return
A(n=2)
Return A(n=2) Return
Flowchart for Recursive FunctionA(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary
search tree, such that the resulting tree has height 6, is .
Note: The height of a tree with a single node is 0.
CS(Set B) 11/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.41 In an adjacency list representation of an undirected simple graph G=(V;E), each edge(u;v)
has two adjacency list entries: [v] in the adjacency list of u, and [u] in the adjacency list of
v. These are called twins of each other. A twin pointer is a pointer from an adjacency list
entry to its twin. IfjEj= m andjVj= n, and the memory size is not a constraint, what is the
time complexity of the most ef?cient algorithm to set the twin pointer in each entry in each
adjacency list?
(A) Q(n
2
)
(B) Q(n+ m)
(C) Q(m
2
)
(D) Q(n
4
)
Q.42 Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA isS
.
II. There exists a regular language A such that for all languages B, A\ B is regular.
Which one of the following isCORRECT?
(A) OnlyI is true
(B) OnlyII is true
(C) BothI andII are true
(D) BothI andII are false
Q.43 Consider the following languages:
L
1
=fa
n
b
m
c
n+m
: m;n 1g
L
2
=fa
n
b
n
c
2n
: n 1g
Which one of the following isTRUE?
(A) Both L
1
and L
2
are context-free.
(B) L
1
is context-free while L
2
is not context-free.
(C) L
2
is context-free while L
1
is not context-free.
(D) Neither L
1
nor L
2
is context-free.
CS(Set B) 12/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.44 Consider the following languages.
L
1
= fhMij M takes at least 2016 steps on some inputg;
L
2
= fhMij M takes at least 2016 steps on all inputsg and
L
3
= fhMij M acceptseg;
where for each Turing machine M,hMi denotes a speci?c encoding of M. Which one of the
following isTRUE?
(A) L
1
is recursive and L
2
;L
3
are not recursive
(B) L
2
is recursive and L
1
;L
3
are not recursive
(C) L
1
;L
2
are recursive and L
3
is not recursive
(D) L
1
;L
2
;L
3
are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S ! AB
A ! Aa j b
B ! c
(B) S ! Ab j Bb j c
A ! Bd j e
B ! e
(C) S ! Aa j B
A ! Bb j Sc j e
B ! d
(D) S ! Aa j Bb j c
A ! Bd j e
B ! Ae j e
CS(Set B) 13/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array
declaration. The dimension of the array is at least one. For example,
int a[10][3];
The grammars use D as the start symbol, and use six terminal symbolsint;id[]num.
GrammarG1 GrammarG2
D!intL; D!intL;
L!id[E L!idE
E!num] E! E[num]
E!num][E E![num]
Which of the grammars correctly generate the declaration mentioned above?
(A) BothG1 andG2
(B) OnlyG1
(C) OnlyG2
(D) NeitherG1 norG2
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given
in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time ?rst.
Process Arrival Time Burst Time
P
1
0 10
P
2
3 6
P
3
7 1
P
4
8 3
The average turn around time of these processes is milliseconds.
CS(Set B) 14/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.48 Consider the following two-process synchronization solution.
Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;
Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;
The shared variableturn is initialized to zero. Which one of the following isTRUE?
(A) This is a correct two-process synchronization solution.
(B) This solution violates mutual exclusion requirement.
(C) This solution violates progress requirement.
(D) This solution violates bounded wait requirement.
Q.49 Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S)
increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in
some order. The largest initial value of S for which at least one P(S) operation will remain
blocked is .
CS(Set B) 15/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.50 A ?le system uses an in-memory cache to cache disk blocks. The miss rate of the cache is
shown in the ?gure. The latency to read a block from the cache is 1 ms and to read a block
from the disk is 10 ms. Assume that the cost of checking whether a block exists in the cache
is negligible. Available cache sizes are in multiples of 10 MB.
10 20 30 40 50
10
60 70 80 90
20
30
40
50
60
70
80
90
0
0
Miss rate (%)
Cache size (MB)
The smallest cache size required to ensure an average read latency of less than 6 ms is
MB.
Q.51 Consider the following database schedule with two transactions, T
1
and T
2
.
S= r
2
(X); r
1
(X); r
2
(Y); w
1
(X); r
1
(Y); w
2
(X); a
1
; a
2
where r
i
(Z) denotes a read operation by transaction T
i
on a variable Z, w
i
(Z) denotes a write
operation by T
i
on a variable Z and a
i
denotes an abort by transaction T
i
.
Which one of the following statements about the above schedule isTRUE?
(A) S is non-recoverable
(B) S is recoverable, but has a cascading abort
(C) S does not have a cascading abort
(D) S is strict
CS(Set B) 16/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.52 Consider the following database table named water_schemes :
water_schemes
scheme_no district_name capacity
1 Ajmer 20
1 Bikaner 10
2 Bikaner 10
3 Bikaner 20
1 Churu 10
2 Churu 20
1 Dungargarh 10
The number of tuples returned by the following SQL query is .
with total(name, capacity) as
select district_name, sum(capacity)
from water_schemes
groupby district_name
with total_avg(capacity) as
select avg(capacity)
from total
select name
from total, total_avg
where total.capacity total_avg.capacity
Q.53 A network has a data transmission bandwidth of 20 10
6
bits per second. It uses CSMA/CD
in the MAC layer. The maximum signal propagation time from one node to another node is
40 microseconds. The minimum size of a frame in the network is bytes.
CS(Set B) 17/18
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.54 For the IEEE 802.11 MAC protocol for wireless communication, which of the following
statements is/areTRUE?
I. At least three non-overlapping channels are available for transmissions.
II. The RTS-CTS mechanism is used for collision detection.
III. Unicast frames are ACKed.
(A) All I, II, and III
(B) I and III only
(C) II and III only
(D) II only
Q.55 Consider a 12810
3
bits/second satellite communication link with one way propagation delay
of 150 milliseconds. Selective retransmission (repeat) protocol is used on this link to send
data with a frame size of 1 kilobyte. Neglect the transmission time of acknowledgement. The
minimum number of bits required for the sequence number ?eld to achieve 100% utilization
is .
CS(Set B) 18/18
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This post was last modified on 18 December 2019