# Electrical Engineering - GATE 2014 Paper Solution

Question No. 1

## 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.

Question No. 2

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 __________.

Question No. 3

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

Question No. 4

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

Question No. 5

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

Question No. 6

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?

Question No. 7

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?

Question No. 8

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 _________.

Question No. 9

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?

Question No. 10

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? _____________

Question No. 11

Given a system of equations:

$x+2y+2z={b}_{1}$

$5x+y+3z={b}_{2}$

Which of the following is true regarding its solutions

Question No. 12

Let $f\left(x\right)=x{e}^{-x}$. The maximum value of the function in the interval $\left(0,\infty \right)$ is

Question No. 13

The solution for the differential equation

$\frac{{d}^{2}x}{d{t}^{2}}=-9x,$

with initial conditions $x\left(0\right)=1$ and ${\overline{)\frac{dx}{dt}}}_{t=0}=1$ is

Question No. 14

Let $X\left(S\right)=\frac{3s+5}{{s}^{2}+10s+21}$ be the Laplace Transform of a signal $x\left(t\right)$. Then, $x\left({0}^{+}\right)$ is

Question No. 15

Let S be the set of points in the complex plane corresponding to the unit circle. (That is, $S=\left\{z:\left|z\right|=1\right\}$). Consider the function $f\left(z\right)=z{z}^{*}$ where z* denotes the complex conjugate of z. The $f\left(z\right)$ maps S to which one of the following in the complex plane

Question No. 16

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________.

Question No. 17

C0 is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity ${\mathit{\in }}_{r}$, the expression for the modified capacitance is

Question No. 18

A combination of 1 µF capacitor with an initial voltage${\nu }_{c}\left(0\right)=-2\nu$ in series with a 100 O resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage vs across the current source over the next few seconds?

$x\left(t\right)$ is nonzero only for ${T}_{x} , and similarly, $y\left(t\right)$ is nonzero only for ${T}_{y}. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?