# Computer Science and Information Technology - GATE 2014 Paper Solution

### SET-1

Which of the following options is the closest in meaning to the phrase underlined in the sentence below?
It is fascinating to see life forms cope with varied environmental conditions.

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Choose the most appropriate word from the options given below to complete the following sentence.
He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________.

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In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?

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If (z + 1/z)2 = 98, compute (z2 + 1/z2).

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The roots of ax2 + bx+ c = 0 are real and positive. a, b and c are real. Then ax2 + b|x| + c = 0 has

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The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures.
What can be inferred from this passage?

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Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy.
On which of the following assumptions does the statement above rely?

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Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.

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In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

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When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________

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Consider the statement
“Not all that glitters is gold”
Predicate glitter(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?

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Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .

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Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?

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Consider the following system of equations:

3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0

The number of solutions for this system is __________________

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The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is ___________________.

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Let the function

$f\left(\theta \right)=\left|\begin{array}{ccc}\mathrm{sin}\theta & \mathrm{cos}\theta & \mathrm{tan}\theta \\ \mathrm{sin}\left(\mathrm{\pi }}{6}\right)& \mathrm{cos}\left(\mathrm{\pi }}{6}\right)& \mathrm{tan}\left(\mathrm{\pi }}{6}\right)\\ \mathrm{sin}\left(\mathrm{\pi }}{3}\right)& \mathrm{cos}\left(\mathrm{\pi }}{3}\right)& \mathrm{tan}\left(\mathrm{\pi }}{3}\right)\end{array}\right|$

where $\theta \in \left[\begin{array}{cc}\frac{\pi }{6},& \frac{\pi }{3}\end{array}\right]$ and $f\text{'}\left(\theta \right)$ denote the derivative of f with respect to θ. Which of the following statements is/are TRUE?

(I) There exists $\theta \in \left[\begin{array}{cc}\frac{\pi }{6},& \frac{\pi }{3}\end{array}\right]$ such that $f\text{'}\left(\theta \right)$=0.

(II) There exists $\theta \in \left[\begin{array}{cc}\frac{\pi }{6},& \frac{\pi }{3}\end{array}\right]$ such that $f\text{'}\left(\theta \right)$≠0.

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Consider the following Boolean expression for F:

$F\left(P,Q,R,S\right)=PQ+\overline{P}QR+\overline{P}Q\overline{R}S$

The minimal sum-of-products form of F is

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The base (or radix) of the number system such that the following equation holds is____________.

$\frac{312}{20}=13.1$

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A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________.

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Consider the following program in C language:

#include <stdio.h>
main()
{
int i;
int *pi = &i;
scanf(“%d”,pi);
printf(“%d\n”, i+5);
}

Which one of the following statements is TRUE?