# Computer Science and Information Technology - GATE 2016 Paper Solution

#### SET - 1

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

A rewording of something written or spoken is a ______________.

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.

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

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 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?

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?

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

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

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 ________.

Let  p, q, r, s represent the following propositions.

: ∈ {8,9,10,11,12}

: x is a composite number

: x is a perfect square

: x is a prime number

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

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 $a_n$?

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

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 of a is .

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

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

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