Firstranker's choice
GATE 2016
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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.
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(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
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(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."
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The sentence above is an example of a ___________ statement.
(A) figurative
(B) collateral
(C) literal
Q.4
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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
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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
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(D) 96
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?
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(A) Elegance
(B) Executive
(C) Smooth
(D) Soft
Q.7
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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.
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(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
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III. S loses to P only sometime
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
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(A) (i) only
(B) (ii) only
(C) (i) and (ii)
(D) neither (i) nor (ii)
Q.9
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If f(x) = 2x7 + 3x – 5, which of the following is a factor of f(x)?
(A) (x3+8)
(B) (x-1)
(C) (2x-5)
(D) (x+1)
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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
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(D) 92.02
END OF THE QUESTION PAPER
GATE 2016
COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
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Q. 1 - Q. 25 carry one mark each.
Q.1
Let p,q, r, s represent the following propositions.
p: x ? {8,9,10,11,12}
q: x is a composite number
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r: x is a perfect square
s: x is a prime number
The integer x = 2 which satisfies ¬((p? q) ? (¬r? ¬s)) is ___________.
Q.2
Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an?
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(A) an = an-1+2an-2
(B) an = an-1+an-2
(C) an = 2an-1+an-2
(D) an = 2an-1+2an-2
Q.3
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The value of the integral ?-88 e -4x² dx is ___________.
Q.4
A probability density function on the interval [a, 1] is given by 1/x² and outside this interval the value of the function is zero. The value of a is ___________.
Q.5
Two eigenvalues of a 3 × 3 real matrix P are (2+v-4) and (2-v-4), The determinant of P is ___________.
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Q.6
Consider the Boolean operator # with the following properties:
x#0 = x, x#1 = x', x#x = 0 and x#x' = 1. Then x#y is equivalent to
(A) xy+x'y'
(B) xy'+x'y
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(C) x'y+xy'
(D) xy+xy
Q.7
The 16-bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is ___________.
Q.8
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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 flip-flops required to implement this counter is ___________ bits.
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 efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)?
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(A) Both operations can be performed in O(1) time
(B) At most one operation can be performed in O(1) time but the worst case time for the other operation will be O(n)
(C) The worst case time complexity for both operations will be O(n)
(D) Worst case time complexity for both operations will be O(logn)
Q.11
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Consider the following directed graph:
Firstranker's choice
GATE 2016
Q. 1 – Q. 5 carry one mark each.
--- Content provided by FirstRanker.com ---
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.
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(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
--- Content provided by FirstRanker.com ---
(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.
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(A) figurative
(B) collateral
(C) literal
Q.4
If 'relftaga' means carefree, 'otaga' means careful and 'fertaga' means careless, which of the following could mean ‘aftercare'?
--- Content provided by FirstRanker.com ---
(A) zentaga
(B) tagafer
(C) tagazen
(D) relffer
Q.5
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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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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
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(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.
--- Content provided by FirstRanker.com ---
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.
--- Content provided by FirstRanker.com ---
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 sometime
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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
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(B) (ii) only
(C) (i) and (ii)
(D) neither (i) nor (ii)
Q.9
If f(x) = 2x7 + 3x – 5, which of the following is a factor of f(x)?
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(A) (x3+8)
(B) (x-1)
(C) (2x-5)
(D) (x+1)
Q.10
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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
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END OF THE QUESTION PAPER
GATE 2016
COMPUTER SCIENCE AND INFORMATION TECHNOLOGY
Q. 1 - Q. 25 carry one mark each.
--- Content provided by FirstRanker.com ---
Q.1
Let p,q, r, s represent the following propositions.
p: x ? {8,9,10,11,12}
q: x is a composite number
r: x is a perfect square
--- Content provided by FirstRanker.com ---
s: x is a prime number
The integer x = 2 which satisfies ¬((p? q) ? (¬r? ¬s)) is ___________.
Q.2
Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an?
(A) an = an-1+2an-2
--- Content provided by FirstRanker.com ---
(B) an = an-1+an-2
(C) an = 2an-1+an-2
(D) an = 2an-1+2an-2
Q.3
The value of the integral ?-88 e -4x² dx is ___________.
--- Content provided by FirstRanker.com ---
Q.4
A probability density function on the interval [a, 1] is given by 1/x² and outside this interval the value of the function is zero. The value of a is ___________.
Q.5
Two eigenvalues of a 3 × 3 real matrix P are (2+v-4) and (2-v-4), The determinant of P is ___________.
Q.6
--- Content provided by FirstRanker.com ---
Consider the Boolean operator # with the following properties:
x#0 = x, x#1 = x', x#x = 0 and x#x' = 1. Then x#y is equivalent to
(A) xy+x'y'
(B) xy'+x'y
(C) x'y+xy'
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(D) xy+xy
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 flip-flops required to implement this counter is ___________ bits.
--- Content provided by FirstRanker.com ---
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 efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)?
(A) Both operations can be performed in O(1) time
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(B) At most one operation can be performed in O(1) time but the worst case time for the other operation will be O(n)
(C) The worst case time complexity for both operations will be O(n)
(D) Worst case time complexity for both operations will be O(logn)
Q.11
Consider the following directed graph:
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