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.

Question No. 2

A rewording of something written or spoken is a ______________.

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.

Question No. 4

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?

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 __________.

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?

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?

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

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)?

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 ________.

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 .

Question No. 12

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 $a_n$?

Question No. 13

$\style{font-family:'Times New Roman'}{\lim_{x\rightarrow4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_.}$

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 .

Question No. 15

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

Question No. 16

Consider the Boolean operator # with the following properties:

and . Then x#y is equivalent to

Question No. 17

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

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 .