Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 CS01 Computer Sc. and Information Technology Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.40 G=(V;E) is an undirected simple graph in which each edge has a distinct weight, and e is a
particular edge of G. Which of the following statements about the minimum spanning trees
(MSTs) ofG is/areTRUE?
I. Ife is the lightest edge of some cycle inG, then every MST ofG includese
II. Ife is the heaviest edge of some cycle inG, then every MST ofG excludese
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns
the element at the head of the queueQwithout removing it fromQ. SimilarlyTop(S) returns
the element at the top ofSwithout removing it fromS. Consider the algorithm given below.
whileQisnotEmpty do
ifSisEmptyORTop(S)Head(Q)then
x :=Dequeue(Q);
Push(S;x);
else
x :=Pop(S);
Enqueue(Q;x);
end
end
The maximum possible number of iterations of the while loop in the algorithm is
.
Q.42 Consider the following context-free grammars:
G
1
: S!aSjB; B!bjbB
G
2
: S!aAjbB; A!aAjBje; B!bBje
Which one of the following pairs of languages is generated byG
1
andG
2
, respectively?
(A)fa
m
b
n
jm> 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(B)fa
m
b
n
jm> 0 andn> 0g andfa
m
b
n
jm> 0 orn 0g
(C)fa
m
b
n
jm 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(D)fa
m
b
n
jm 0 andn> 0g andfa
m
b
n
jm> 0 orn> 0g
CS(Set A) 13/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.40 G=(V;E) is an undirected simple graph in which each edge has a distinct weight, and e is a
particular edge of G. Which of the following statements about the minimum spanning trees
(MSTs) ofG is/areTRUE?
I. Ife is the lightest edge of some cycle inG, then every MST ofG includese
II. Ife is the heaviest edge of some cycle inG, then every MST ofG excludese
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns
the element at the head of the queueQwithout removing it fromQ. SimilarlyTop(S) returns
the element at the top ofSwithout removing it fromS. Consider the algorithm given below.
whileQisnotEmpty do
ifSisEmptyORTop(S)Head(Q)then
x :=Dequeue(Q);
Push(S;x);
else
x :=Pop(S);
Enqueue(Q;x);
end
end
The maximum possible number of iterations of the while loop in the algorithm is
.
Q.42 Consider the following context-free grammars:
G
1
: S!aSjB; B!bjbB
G
2
: S!aAjbB; A!aAjBje; B!bBje
Which one of the following pairs of languages is generated byG
1
andG
2
, respectively?
(A)fa
m
b
n
jm> 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(B)fa
m
b
n
jm> 0 andn> 0g andfa
m
b
n
jm> 0 orn 0g
(C)fa
m
b
n
jm 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(D)fa
m
b
n
jm 0 andn> 0g andfa
m
b
n
jm> 0 orn> 0g
CS(Set A) 13/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.43 Consider the transition diagram of a PDA given below with input alphabet S=fa;bg and
stack alphabetG=fX;Zg. Z is the initial stack symbol. Let L denote the language accepted
by the PDA.
b;X=e e;Z=Z
b;X=e a;Z=XZ
a;X=XX
Which one of the following isTRUE?
(A) L=fa
n
b
n
jn 0g and is not accepted by any ?nite automata
(B) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is not accepted by any deterministic PDA
(C) L is not accepted by any Turing machine that halts on every input
(D) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is deterministic context-free
Q.44 Let X be a recursive language andY be a recursively enumerable but not recursive language.
LetW andZ be two languages such thatY reduces toW, andZ reduces toX (reduction means
the standard many-one reduction). Which one of the following statements isTRUE?
(A) W can be recursively enumerable andZ is recursive.
(B) W can be recursive andZ is recursively enumerable.
(C) W is not recursively enumerable andZ is recursive.
(D) W is not recursively enumerable andZ is not recursive.
Q.45 The attributes of three arithmetic operators in some programming language are given below.
Operator Precedence Associativity Arity
+ High Left Binary
Medium Right Binary
Low Left Binary
The value of the expression2 5+1 73 in this language is .
CS(Set A) 14/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.40 G=(V;E) is an undirected simple graph in which each edge has a distinct weight, and e is a
particular edge of G. Which of the following statements about the minimum spanning trees
(MSTs) ofG is/areTRUE?
I. Ife is the lightest edge of some cycle inG, then every MST ofG includese
II. Ife is the heaviest edge of some cycle inG, then every MST ofG excludese
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns
the element at the head of the queueQwithout removing it fromQ. SimilarlyTop(S) returns
the element at the top ofSwithout removing it fromS. Consider the algorithm given below.
whileQisnotEmpty do
ifSisEmptyORTop(S)Head(Q)then
x :=Dequeue(Q);
Push(S;x);
else
x :=Pop(S);
Enqueue(Q;x);
end
end
The maximum possible number of iterations of the while loop in the algorithm is
.
Q.42 Consider the following context-free grammars:
G
1
: S!aSjB; B!bjbB
G
2
: S!aAjbB; A!aAjBje; B!bBje
Which one of the following pairs of languages is generated byG
1
andG
2
, respectively?
(A)fa
m
b
n
jm> 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(B)fa
m
b
n
jm> 0 andn> 0g andfa
m
b
n
jm> 0 orn 0g
(C)fa
m
b
n
jm 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(D)fa
m
b
n
jm 0 andn> 0g andfa
m
b
n
jm> 0 orn> 0g
CS(Set A) 13/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.43 Consider the transition diagram of a PDA given below with input alphabet S=fa;bg and
stack alphabetG=fX;Zg. Z is the initial stack symbol. Let L denote the language accepted
by the PDA.
b;X=e e;Z=Z
b;X=e a;Z=XZ
a;X=XX
Which one of the following isTRUE?
(A) L=fa
n
b
n
jn 0g and is not accepted by any ?nite automata
(B) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is not accepted by any deterministic PDA
(C) L is not accepted by any Turing machine that halts on every input
(D) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is deterministic context-free
Q.44 Let X be a recursive language andY be a recursively enumerable but not recursive language.
LetW andZ be two languages such thatY reduces toW, andZ reduces toX (reduction means
the standard many-one reduction). Which one of the following statements isTRUE?
(A) W can be recursively enumerable andZ is recursive.
(B) W can be recursive andZ is recursively enumerable.
(C) W is not recursively enumerable andZ is recursive.
(D) W is not recursively enumerable andZ is not recursive.
Q.45 The attributes of three arithmetic operators in some programming language are given below.
Operator Precedence Associativity Arity
+ High Left Binary
Medium Right Binary
Low Left Binary
The value of the expression2 5+1 73 in this language is .
CS(Set A) 14/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals
{S, A} and terminals {a,b}.
S ! aA { print 1 }
S ! a { print 2 }
A ! Sb { print 3 }
Using the above SDTS, the output printed by a bottom-up parser, for the inputaab is:
(A) 1 3 2
(B) 2 2 3
(C) 2 3 1
(D) syntax error
Q.47 Consider a computer system with 40-bit virtual addressing and page size of sixteen
kilobytes. If the computer system has a one-level page table per process and each page table
entry requires 48 bits, then the size of the per-process page table is megabytes.
Q.48 Consider a disk queue with requests for I/O to blocks on cylinders 47, 38, 121, 191, 87, 11,
92, 10. The C-LOOK scheduling algorithm is used. The head is initially at cylinder number
63, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered
from 0 to 199. The total head movement (in number of cylinders) incurred while servicing
these requests is .
Q.49 Consider a computer system with ten physical page frames. The system is provided with
an access sequence (a
1
;a
2
;:::;a
20
;a
1
;a
2
;:::;a
20
), where each a
i
is a distinct virtual page
number. The difference in the number of page faults between the last-in-?rst-out page
replacement policy and the optimal page replacement policy is .
CS(Set A) 15/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.40 G=(V;E) is an undirected simple graph in which each edge has a distinct weight, and e is a
particular edge of G. Which of the following statements about the minimum spanning trees
(MSTs) ofG is/areTRUE?
I. Ife is the lightest edge of some cycle inG, then every MST ofG includese
II. Ife is the heaviest edge of some cycle inG, then every MST ofG excludese
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns
the element at the head of the queueQwithout removing it fromQ. SimilarlyTop(S) returns
the element at the top ofSwithout removing it fromS. Consider the algorithm given below.
whileQisnotEmpty do
ifSisEmptyORTop(S)Head(Q)then
x :=Dequeue(Q);
Push(S;x);
else
x :=Pop(S);
Enqueue(Q;x);
end
end
The maximum possible number of iterations of the while loop in the algorithm is
.
Q.42 Consider the following context-free grammars:
G
1
: S!aSjB; B!bjbB
G
2
: S!aAjbB; A!aAjBje; B!bBje
Which one of the following pairs of languages is generated byG
1
andG
2
, respectively?
(A)fa
m
b
n
jm> 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(B)fa
m
b
n
jm> 0 andn> 0g andfa
m
b
n
jm> 0 orn 0g
(C)fa
m
b
n
jm 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(D)fa
m
b
n
jm 0 andn> 0g andfa
m
b
n
jm> 0 orn> 0g
CS(Set A) 13/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.43 Consider the transition diagram of a PDA given below with input alphabet S=fa;bg and
stack alphabetG=fX;Zg. Z is the initial stack symbol. Let L denote the language accepted
by the PDA.
b;X=e e;Z=Z
b;X=e a;Z=XZ
a;X=XX
Which one of the following isTRUE?
(A) L=fa
n
b
n
jn 0g and is not accepted by any ?nite automata
(B) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is not accepted by any deterministic PDA
(C) L is not accepted by any Turing machine that halts on every input
(D) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is deterministic context-free
Q.44 Let X be a recursive language andY be a recursively enumerable but not recursive language.
LetW andZ be two languages such thatY reduces toW, andZ reduces toX (reduction means
the standard many-one reduction). Which one of the following statements isTRUE?
(A) W can be recursively enumerable andZ is recursive.
(B) W can be recursive andZ is recursively enumerable.
(C) W is not recursively enumerable andZ is recursive.
(D) W is not recursively enumerable andZ is not recursive.
Q.45 The attributes of three arithmetic operators in some programming language are given below.
Operator Precedence Associativity Arity
+ High Left Binary
Medium Right Binary
Low Left Binary
The value of the expression2 5+1 73 in this language is .
CS(Set A) 14/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals
{S, A} and terminals {a,b}.
S ! aA { print 1 }
S ! a { print 2 }
A ! Sb { print 3 }
Using the above SDTS, the output printed by a bottom-up parser, for the inputaab is:
(A) 1 3 2
(B) 2 2 3
(C) 2 3 1
(D) syntax error
Q.47 Consider a computer system with 40-bit virtual addressing and page size of sixteen
kilobytes. If the computer system has a one-level page table per process and each page table
entry requires 48 bits, then the size of the per-process page table is megabytes.
Q.48 Consider a disk queue with requests for I/O to blocks on cylinders 47, 38, 121, 191, 87, 11,
92, 10. The C-LOOK scheduling algorithm is used. The head is initially at cylinder number
63, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered
from 0 to 199. The total head movement (in number of cylinders) incurred while servicing
these requests is .
Q.49 Consider a computer system with ten physical page frames. The system is provided with
an access sequence (a
1
;a
2
;:::;a
20
;a
1
;a
2
;:::;a
20
), where each a
i
is a distinct virtual page
number. The difference in the number of page faults between the last-in-?rst-out page
replacement policy and the optimal page replacement policy is .
CS(Set A) 15/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.50 Consider the following proposed solution for the critical section problem. There are n
processes: P
0
:::P
n 1
. In the code, function pmax returns an integer not smaller than any
of its arguments. For alli,t[i] is initialized to zero.
Code forP
i
:
do {
c[i]=1; t[i] = pmax(t[0],:::,t[n-1])+1; c[i]=0;
for every j 6= i in {0,:::,n-1} {
while (c[j]);
while (t[j] != 0 && t[j]<=t[i]);
}
Critical Section;
t[i]=0;
Remainder Section;
} while (true);
Which one of the following isTRUE about the above solution?
(A) At most one process can be in the critical section at any time
(B) The bounded wait condition is satis?ed
(C) The progress condition is satis?ed
(D) It cannot cause a deadlock
Q.51 Consider the following two phase locking protocol. Suppose a transaction T accesses (for
read or write operations), a certain set of objectsfO
1
;:::;O
k
g. This is done in the following
manner:
Step1. T acquires exclusive locks toO
1
, . . . ,O
k
in increasing order of their addresses.
Step2. The required operations are performed.
Step3. All locks are released.
This protocol will
(A) guarantee serializability and deadlock-freedom
(B) guarantee neither serializability nor deadlock-freedom
(C) guarantee serializability but not deadlock-freedom
(D) guarantee deadlock-freedom but not serializability
CS(Set A) 16/17
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.1-Q.25carryonemarkeach.
Q.1 Let p;q;r;s represent the following propositions.
p: x2f8;9;10;11;12g
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integerx 2 which satis?es:((p)q)^(:r_:s)) is .
Q.2 Let a
n
be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation fora
n
?
(A) a
n
=a
n 1
+ 2a
n 2
(B) a
n
=a
n 1
+a
n 2
(C) a
n
= 2a
n 1
+a
n 2
(D) a
n
= 2a
n 1
+ 2a
n 2
Q.3
lim
x!4
sin(x 4)
x 4
= :
Q.4 A probability density function on the interval [a;1] is given by 1=x
2
and outside this interval
the value of the function is zero. The value ofa is .
Q.5 Two eigenvalues of a 3 3 real matrix P are (2+
p
1) and 3. The determinant of P is
.
CS(Set A) 1/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.6 Consider the Boolean operator # with the following properties:
x#0=x,x#1= ? x,x#x= 0 andx# ? x= 1. Thenx#y is equivalent to
(A) x ? y+ ? xy
(B) x ? y+ ? x ? y
(C) ? xy+xy
(D) xy+ ? x ? y
Q.7 The 16-bit 2?s complement representation of an integer is 1111 1111 1111 0101; its decimal
representation is .
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then
repeats. The minimum number of J-K ?ip-?ops required to implement this counter is
.
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable
(a word consists of two bytes). The size of the address bus of the processor is at least
bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed ef?ciently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?
(A) Both operations can be performed inO(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for
the other operation will beW(n)
(C) The worst case time complexity for both operations will beW(n)
(D) Worst case time complexity for both operations will beW(logn)
CS(Set A) 2/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.11 Consider the following directed graph:
a
b c
f
e d
The number of different topological orderings of the vertices of the graph is .
Q.12 Consider the following C program.
void f(int, short);
void main()
{
int i = 100;
short s = 12;
short *p = &s;
__________ ; // call to f()
}
Which one of the following expressions, when placed in the blank above, will NOT result in
a type checking error?
(A) f(s,*s)
(B) i = f(i,s)
(C) f(i,*s)
(D) f(i,*p)
CS(Set A) 3/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.13 The worst case running times ofInsertionsort,Mergesort andQuicksort, respectively, are:
(A) Q(nlogn),Q(nlogn), andQ(n
2
)
(B) Q(n
2
),Q(n
2
), andQ(nlogn)
(C) Q(n
2
),Q(nlogn), andQ(nlogn)
(D) Q(n
2
),Q(nlogn), andQ(n
2
)
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every
edge weight is increased by the same value, then which of the following statements is/are
TRUE?
P: Minimum spanning tree ofG does not change
Q: Shortest path between any pair of vertices does not change
(A) P only
(B) Q only
(C) Neither P nor Q
(D) Both P and Q
CS(Set A) 4/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.15 Consider the following C program.
#include
void mystery(int *ptra, int *ptrb) {
int *temp;
temp = ptrb;
ptrb = ptra;
ptra = temp;
}
int main() {
int a=2016, b=0, c=4, d=42;
mystery(&a, &b);
if (a < c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d\n", a);
}
The output of the program is .
Q.16 Which of the following languages is generated by the given grammar?
S ! aSjbSj e
(A)fa
n
b
m
jn;m 0g
(B)fw2fa;bg
j w has equal number of a?s and b?sg
(C)fa
n
jn 0g[fb
n
jn 0g[fa
n
b
n
jn 0g
(D)fa;bg
CS(Set A) 5/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.17 Which of the following decision problems are undecidable?
I. Given NFAsN
1
andN
2
, isL(N
1
)\L(N
2
)=F?
II. Given a CFGG=(N;S;P;S) and a stringx2S
, doesx2L(G)?
III. Given CFGsG
1
andG
2
, isL(G
1
)=L(G
2
)?
IV . Given a TMM, isL(M)=F?
(A) I and IV only
(B) II and III only
(C) III and IV only
(D) II and IV only
Q.18 Which one of the following regular expressions represents the language: the set of all binary
stringshavingtwoconsecutive 0sandtwoconsecutive 1s?
(A) (0+ 1)
0011(0+ 1)
+(0+ 1)
1100(0+ 1)
(B) (0+ 1)
(00(0+ 1)
11+ 11(0+ 1)
00)(0+ 1)
(C) (0+ 1)
00(0+ 1)
+(0+ 1)
11(0+ 1)
(D) 00(0+ 1)
11+ 11(0+ 1)
00
Q.19 Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static
singleassignment form is .
CS(Set A) 6/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths
submitted at the same time to a computer system. Which one of the following process
scheduling algorithms would minimize the average waiting time in the ready queue?
(A) Shortest remaining time ?rst
(B) Round-robin with time quantum less than the shortest CPU burst
(C) Uniform random
(D) Highest priority ?rst with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes
V ,W,X,Y ,Z and primary keyVY ?
(A) VXYZ
(B) VWXZ
(C) VWXY
(D) VWXYZ
Q.22 Which one of the following isNOT a part of the ACID properties of database transactions?
(A) Atomicity
(B) Consistency
(C) Isolation
(D) Deadlock-freedom
CS(Set A) 7/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following
functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! TITLE
(VOLUME, NUMBER) ! YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) ! PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satis?es, but the old one does not?
(A) 1NF
(B) 2NF
(C) 3NF
(D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another
one?
(A) DNS
(B) ARP
(C) DHCP
(D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3
(A) (i) and (ii) only
(B) (ii) and (iii) only
(C) (ii) and (iv) only
(D) (iv) only
CS(Set A) 8/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.26-Q.55carrytwomarkseach.
Q.26 The coef?cient ofx
12
in(x
3
+x
4
+x
5
+x
6
+)
3
is .
Q.27 Consider the recurrence relation a
1
= 8, a
n
= 6n
2
+ 2n+a
n 1
. Let a
99
=K 10
4
. The value
ofK is .
Q.28 A function f :N
+
!N
+
, de?ned on the set of positive integersN
+
, satis?es the following
properties:
f(n)= f(n=2) ifnis even
f(n)= f(n+ 5) ifnis odd
LetR=fij9j : f(j)=ig be the set of distinct values that f takes. The maximum possible size
ofR is .
Q.29 Consider the following experiment.
Step1. Flip a fair coin twice.
Step2. If the outcomes are (TAILS, HEADS) then outputY and stop.
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.
The probability that the output of the experiment is Y is (up to two decimal places)
.
CS(Set A) 9/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the ?gure.
MUX
2?to?1
0
1
0
1
0
MUX
2?to?1
X
R
R
P Q
s s
The minimal sum of products form of the outputX is
(A)
?
P
?
Q+PQR
(B)
?
PQ+QR
(C) PQ+
?
P
?
QR
(D)
?
Q
?
R+PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to
transfer a ?le of 29,154 kilobytes from disk to main memory. The memory is byte addressable.
The minimum number of times the DMA controller needs to get the control of the system bus
from the processor to transfer the ?le from the disk to main memory is .
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The ?rst
stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving
two stages with respective delays 600 and 350 picoseconds. The throughput increase of the
pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at
most two. The time to perform addition using this adder is
(A) Q(1)
(B) Q(log(n))
(C) Q(
p
n)
(D) Q(n)
CS(Set A) 10/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.34 The following function computes the maximum value contained in an integer arrayp[] of size
n (n >= 1).
int max(int *p, int n) {
int a=0, b=n-1;
while (__________) {
if (p[a] <= p[b]) { a = a+1; }
else { b = b-1; }
}
return p[a];
}
The missing loop condition is
(A) a != n
(B) b != 0
(C) b > (a + 1)
(D) b != a
Q.35 What will be the output of the following C program?
void count(int n){
static int d=1;
printf("%d ", n);
printf("%d ", d);
d++;
if(n>1) count(n-1);
printf("%d ", d);
}
void main(){
count(3);
}
(A) 3 1 2 2 1 3 4 4 4
(B) 3 1 2 1 1 1 2 2 2
(C) 3 1 2 2 1 3 4
(D) 3 1 2 1 1 1 2
CS(Set A) 11/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.36 What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x) {x = x * a; print(x);}
void m(y) {a = 1; a = y - a; n(a); print(a);}
void main() {m(a);}
(A) 6, 2
(B) 6, 6
(C) 4, 2
(D) 4, 4
Q.37 An operator delete(i) for a binary heap data structure is to be designed to delete the item in
the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index
of the array. If the heap tree has depth d (number of edges on the path from the root to the
farthest leaf), then what is the time complexity to re-?x the heap ef?ciently after the removal
of the element?
(A) O(1)
(B) O(d) but notO(1)
(C) O(2
d
) but notO(d)
(D) O(d 2
d
) but notO(2
d
)
Q.38 Consider the weighted undirected graph with 4 vertices, where the weight of edgefi;jg is
given by the entryW
ij
in the matrixW.
W =
2
6
6
4
0 2 8 5
2 0 5 8
8 5 0 x
5 8 x 0
3
7
7
5
The largest possible integer value ofx, for which at least one shortest path between some pair
of vertices will contain the edge with weightx is .
Q.39 Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2,
3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can
have is .
CS(Set A) 12/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.40 G=(V;E) is an undirected simple graph in which each edge has a distinct weight, and e is a
particular edge of G. Which of the following statements about the minimum spanning trees
(MSTs) ofG is/areTRUE?
I. Ife is the lightest edge of some cycle inG, then every MST ofG includese
II. Ife is the heaviest edge of some cycle inG, then every MST ofG excludese
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns
the element at the head of the queueQwithout removing it fromQ. SimilarlyTop(S) returns
the element at the top ofSwithout removing it fromS. Consider the algorithm given below.
whileQisnotEmpty do
ifSisEmptyORTop(S)Head(Q)then
x :=Dequeue(Q);
Push(S;x);
else
x :=Pop(S);
Enqueue(Q;x);
end
end
The maximum possible number of iterations of the while loop in the algorithm is
.
Q.42 Consider the following context-free grammars:
G
1
: S!aSjB; B!bjbB
G
2
: S!aAjbB; A!aAjBje; B!bBje
Which one of the following pairs of languages is generated byG
1
andG
2
, respectively?
(A)fa
m
b
n
jm> 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(B)fa
m
b
n
jm> 0 andn> 0g andfa
m
b
n
jm> 0 orn 0g
(C)fa
m
b
n
jm 0 orn> 0g andfa
m
b
n
jm> 0 andn> 0g
(D)fa
m
b
n
jm 0 andn> 0g andfa
m
b
n
jm> 0 orn> 0g
CS(Set A) 13/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.43 Consider the transition diagram of a PDA given below with input alphabet S=fa;bg and
stack alphabetG=fX;Zg. Z is the initial stack symbol. Let L denote the language accepted
by the PDA.
b;X=e e;Z=Z
b;X=e a;Z=XZ
a;X=XX
Which one of the following isTRUE?
(A) L=fa
n
b
n
jn 0g and is not accepted by any ?nite automata
(B) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is not accepted by any deterministic PDA
(C) L is not accepted by any Turing machine that halts on every input
(D) L=fa
n
jn 0g[fa
n
b
n
jn 0g and is deterministic context-free
Q.44 Let X be a recursive language andY be a recursively enumerable but not recursive language.
LetW andZ be two languages such thatY reduces toW, andZ reduces toX (reduction means
the standard many-one reduction). Which one of the following statements isTRUE?
(A) W can be recursively enumerable andZ is recursive.
(B) W can be recursive andZ is recursively enumerable.
(C) W is not recursively enumerable andZ is recursive.
(D) W is not recursively enumerable andZ is not recursive.
Q.45 The attributes of three arithmetic operators in some programming language are given below.
Operator Precedence Associativity Arity
+ High Left Binary
Medium Right Binary
Low Left Binary
The value of the expression2 5+1 73 in this language is .
CS(Set A) 14/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.46 Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals
{S, A} and terminals {a,b}.
S ! aA { print 1 }
S ! a { print 2 }
A ! Sb { print 3 }
Using the above SDTS, the output printed by a bottom-up parser, for the inputaab is:
(A) 1 3 2
(B) 2 2 3
(C) 2 3 1
(D) syntax error
Q.47 Consider a computer system with 40-bit virtual addressing and page size of sixteen
kilobytes. If the computer system has a one-level page table per process and each page table
entry requires 48 bits, then the size of the per-process page table is megabytes.
Q.48 Consider a disk queue with requests for I/O to blocks on cylinders 47, 38, 121, 191, 87, 11,
92, 10. The C-LOOK scheduling algorithm is used. The head is initially at cylinder number
63, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered
from 0 to 199. The total head movement (in number of cylinders) incurred while servicing
these requests is .
Q.49 Consider a computer system with ten physical page frames. The system is provided with
an access sequence (a
1
;a
2
;:::;a
20
;a
1
;a
2
;:::;a
20
), where each a
i
is a distinct virtual page
number. The difference in the number of page faults between the last-in-?rst-out page
replacement policy and the optimal page replacement policy is .
CS(Set A) 15/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.50 Consider the following proposed solution for the critical section problem. There are n
processes: P
0
:::P
n 1
. In the code, function pmax returns an integer not smaller than any
of its arguments. For alli,t[i] is initialized to zero.
Code forP
i
:
do {
c[i]=1; t[i] = pmax(t[0],:::,t[n-1])+1; c[i]=0;
for every j 6= i in {0,:::,n-1} {
while (c[j]);
while (t[j] != 0 && t[j]<=t[i]);
}
Critical Section;
t[i]=0;
Remainder Section;
} while (true);
Which one of the following isTRUE about the above solution?
(A) At most one process can be in the critical section at any time
(B) The bounded wait condition is satis?ed
(C) The progress condition is satis?ed
(D) It cannot cause a deadlock
Q.51 Consider the following two phase locking protocol. Suppose a transaction T accesses (for
read or write operations), a certain set of objectsfO
1
;:::;O
k
g. This is done in the following
manner:
Step1. T acquires exclusive locks toO
1
, . . . ,O
k
in increasing order of their addresses.
Step2. The required operations are performed.
Step3. All locks are released.
This protocol will
(A) guarantee serializability and deadlock-freedom
(B) guarantee neither serializability nor deadlock-freedom
(C) guarantee serializability but not deadlock-freedom
(D) guarantee deadlock-freedom but not serializability
CS(Set A) 16/17
GATE 2016 COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q.52 Consider that B wants to send a messagem that is digitally signed to A. Let the pair of private
and public keys for A and B be denoted by K
x
and K
+
x
for x=A;B, respectively. Let K
x
(m)
represent the operation of encryptingm with a keyK
x
andH(m) represent the message digest.
Which one of the following indicates the CORRECT way of sending the message m along
with the digital signature to A?
(A)fm;K
+
B
(H(m))g (B)fm;K
B
(H(m))g (C) fm;K
A
(H(m))g (D) fm;K
+
A
(m)g
Q.53 An IP datagram of size 1000 bytes arrives at a router. The router has to forward this packet on
a link whose MTU (maximum transmission unit) is 100 bytes. Assume that the size of the IP
header is 20 bytes.
The number of fragments that the IP datagram will be divided into for transmission is
.
Q.54 For a host machine that uses the token bucket algorithm for congestion control, the token
bucket has a capacity of 1 megabyte and the maximum output rate is 20 megabytes per second.
Tokens arrive at a rate to sustain output at a rate of 10 megabytes per second. The token bucket
is currently full and the machine needs to send 12 megabytes of data. The minimum time
required to transmit the data is seconds.
Q.55 A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames. Frames
are of size 1000 bytes and the transmission rate at the sender is 80 Kbps (1Kbps = 1000
bits/second). Size of an acknowledgement is 100 bytes and the transmission rate at the receiver
is 8 Kbps. The one-way propagation delay is 100 milliseconds.
Assuming no frame is lost, the sender throughput is bytes/second.
CS(Set A) 17/17
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This post was last modified on 18 December 2019