# Electrical Engineering - GATE 2016 Paper Solution

Question No. 1

#### SET - 1

The man who is now Municipal Commissioner worked as ____________________.

Question No. 2

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

Question No. 3

Find the odd one in the following group of words.

mock, deride, praise, jeer

Question No. 4

Pick the odd one from the following options.

Question No. 5

In a quadratic function, the value of the product of the roots (α,β) is 4. Find the value of

$\frac{{\alpha }^{n}+{\beta }^{n}}{{\alpha }^{-n}+{\beta }^{-n}}$

Question No. 6

A mong 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts is ______________.

Question No. 7

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.

Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions

Question No. 8

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.

Question No. 9

In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

Question No. 10

Choose the correct expression for f(x) given in the graph.

Question No. 11

The maximum value attained by the function $f\left(x\right)=x\left(x-1\right)\left(x-2\right)$ in the interval [1, 2] is _____.

Question No. 12

Consider a 3×3 matrix with every element being equal to 1. Its only non-zero eigenvalue is ____.

Question No. 13

The Laplace Transform of $f\left(t\right)={e}^{2t}\mathrm{sin}\left(5t\right)u\left(t\right)$ is

Question No. 14

A function y(t), such that y(0)=1 and y(1)=3e-1,is a solution of the differential equation $\frac{{d}^{2}y}{d{t}^{2}}+2\frac{dy}{dt}+y=0.$ Then  y(2) is

Question No. 15

The value of the integral

$\oint_c\frac{2z+5}{\left(z-{\displaystyle\frac12}\right)\left(z^2-4z+5\right)}dz$

over the contour taken in the anti-clockwise direction, would be

Question No. 16

The transfer function of a system is The steady state output y(t) is for the input $\mathrm{cos}\left(2t\right)$ The values of respectvely are

Question No. 17

The phase cross-over frequency of the transfer function $G\left(S\right)=\frac{100}{{\left(S+1\right)}^{3}}$ in rad/s is

Question No. 18

Consider a continuous-time system with input $x\left(t\right)$ and output $y\left(t\right)$ given by

$y\left(t\right)=x\left(t\right)\mathrm{cos}\left(t\right)$

This system is

The value of $\int_{-\infty}^{+\infty}e^{-t}\delta\left(2t-2\right)\mathrm{dt}$ where $\delta \left(t\right)$ is the Dirac delta function, is