Computer Science and Information Technology - GATE 2016 Paper Solution

Question No. 1

SET - 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.

(D) I will not leave the place until the minister meets me.

Subject : Language Skills

Question No. 2

A rewording of something written or spoken is a ______________.

(A) paraphrase
(B) paradox
(C) paradigm
(D) paraffin

(A) paraphrase

Subject : Language Skills

Question No. 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

(A) figurative

Subject : Language Skills

Question No. 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

(C) tagazen

Subject : Language Skills

Question No. 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

Show Answer

(D) 96

Subject : Analytical Skills

Question No. 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

Show Answer

(B) Executive

Subject : Analytical Skills

Question No. 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.

Show Answer

(D) Linguistic pluralism is strong evidence of India’s diversity.

Subject : Language Skills

Question No. 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)

Show Answer

(D) neither (i) nor (ii)

Subject : Analytical Skills

Question No. 9

If $\style{font-family:'Times New Roman'}{\mathrm f(x)=2x^7+3x-5}$ which of the following is a factor of f(x)?

(A) $(x^3+8)$
(B) $(x-1)$
(C) $(2x-5)$
(D) $(x+1)$

Show Answer

(B) $(x-1)$

Subject : Analytical Skills

Question No. 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

Show Answer

(B) 46.02

Subject : Analytical Skills

Question No. 11

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

s : x is a prime number

The integer x ≥ 2 which satisfies ¬((p⇒q)∧(¬r∨¬s)) is .

Show Answer

11.0 : 11.0

Explanation :

We wish to make

$ \begin{array}{l}\neg\left(\left(p\Rightarrow q\right)\wedge\left(\neg r\vee\neg s\right)\right)=1\\\Rightarrow\;\;\left(p\Rightarrow q\right)\wedge\left(\neg r\vee\neg s\right)=0\\\Rightarrow\;\;\left(p\Rightarrow q\right)=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...(1)\end{array} $

or $ \;\;\left(p\Rightarrow q\right)=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...(2) $

Now (1) is satisfies only when $p=1$ and $q=0$.

Equation (2) $ \neg r\vee\neg s=0 $ iff $ r\wedge s=1 $

i.e. $ r=1 $ $ s=1 $

i.e. $x$ is a perfect square and $x$ is a prime number. Which is not possible so condition (2) cannot be satiesfied by any $x$.

So condition (1) must be satisfies which $ p=1 $ and $ q=0 $ i.e. $x=\left\{8,\;9,\;10,\;11,\;12\right\}$ and $x$ is not a composite.

Now the only value of $x$ which satisfies this is $x=11$. So correct answer is $x=11$.

Question No. 12

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 for $a_n$?

(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} $

Show Answer

(B) $ a_n=a_{n-1}+a_{n-2} $

Subject : Algorithms

Topic : Divide-and-conquer

Explanation :

Let a_n be the number of n-bit strings that do not contain two consecutive 1's. we wish to develop a recurrence relation for a_n.

Consider 1 bit strings 0, 1

So $ a_1=2 $

Consider 2 bit strings 00, 01, 10, 11

Out of minimum only 00, 01, 10 do not contain two consecutive 1's.

Consider 3 bit strings

Out of minimum six strings only 000, 001, 010, 100 and 101 five strings satisfy do not contain two consecutive 1's.

So $a_3=5$. There numbers $ a_1,\;a_2,\;a_3 $ satisfy clearly only (b) $ a_n=a_{n-1}+a_{n-2} $ correct.

Question No. 13

$\lim\limits_{x\rightarrow4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_.$

Show Answer

1.0 : 1.0

Explanation :

$ \lim\limits_{x\rightarrow4}\frac{\sin(x-4)}{x-4} $

Let x - 4 = t not as x → 4

So the requires limits is $ \lim\limits_{x\rightarrow4}\frac{\sin(t)}t=1 $

Question No. 14

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 of a is .

Show Answer

0.5 : 0.5

Explanation :

Given, $ \;f\left(x\right)=\frac1{x^2}\;\;a\leq x\leq1 $

$ \;\;\;\;\;\;\;=0\;\;\;\;\mathrm{elsewhere} $

So $ \int\limits_a^1f\left(x\right)=1 $

⇒ $ \int\limits_a^1\frac1{x^2}=1 $

⇒ $ \left[\frac{-1}x\right]_a^1=1 $

$ \left[\frac11-\frac1a\right]=1 $

⇒ $ \;\;\;\frac1a=2 $

⇒ $ \;\;\;\;\;a=\frac12=0.5 $

Question No. 15

Two eigenvalues of a 3×3 real matrix P are $(2+\sqrt{-1})$ and 3. The determinant of P is .

Show Answer

15.0 : 15.0

Explanation :

Two eigen values are 2 + i and 3 of $ 3\times3 $ matrix. The third eigen value must be 2 - i

Now $ \prod\lambda_\mathit i=\left|\mathrm A\right| $

⇒ $ \begin{array}{l}\left|\mathrm A\right|=2\left(2+i\right)\left(2-i\right)\times3=\left(4-i^\mathit2\right)\times3\\\;\;\;\;\;=5\times3=15\end{array} $

Question No. 16

Consider the Boolean operator # with the following properties:

$x\#0\;=\;x,\;x\#1\;=\;\overline x,\;x\#x\;=\;0\;and\;x\#\overline x\;=1.$ Then $ x#y $ is equivalent to

(A) $x\overset-y+\overset-xy$
(B) $x\overset-y+\overset-x\overset-y$
(C) $ \overline xy+xy $
(D) $xy+\overset-x\overset-y$

Show Answer

(A) $x\overset-y+\overset-xy$

Subject : Digital Logic

Topic : Boolean Algebra

Explanation :

x	y	x#y
0	0	0
0	1	1
1	0	1
1	1	0

$ \begin{array}{l}x\#0=x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...1\\x\#1=\overline x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...2\\x\#x=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...3\\x\#\overline x=1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...4\\x\#y=x\overline y+\overline xy\end{array} $

Question No. 17

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is .

Show Answer

-11.0 : -11.0

Subject : Digital Logic

Topic : Number representation and computer arithmetic (fixed and floating point)

Question No. 18

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 .

Show Answer

3.0 : 4.0

Subject : Digital Logic

Topic : Combinational and Sequential Circuits

Question No. 19

A processor can support a maximum memory of 4GB, 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.

Show Answer

31.0 : 31.0

Subject : Computer Organization and Architecture

Question No. 20

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
(B) At most one operation can be performed in O (1) time but the worst case time for the other operation will be $\Omega(n)$
(C) The worst case time complexity for both operations will be $\Omega(n)$
(D) Worst case time complexity for both operations will be $\Omega(\log n)$

Show Answer

(A) Both operations can be performed in O (1) time

Subject : Programming and Data Structures

Topic : Queues

Computer Science and Information Technology - GATE 2016 Paper Solution

SET - 1

(D) I will not leave the place until the minister meets me.

(A) paraphrase

(A) figurative

(C) tagazen

(D) 96

(B) Executive

(D) Linguistic pluralism is strong evidence of India’s diversity.

(D) neither (i) nor (ii)

(B) $(x-1)$

(B) 46.02

11.0 : 11.0

(B) $ a_n=a_{n-1}+a_{n-2} $

1.0 : 1.0

0.5 : 0.5

15.0 : 15.0

(A) $x\overset-y+\overset-xy$

-11.0 : -11.0

3.0 : 4.0

31.0 : 31.0

(A) Both operations can be performed in O (1) time

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