# Electrical Engineering - GATE 2015 Paper Solution

Question No. 1

#### SET - 1

Didn’t you buy _________ when you went shopping?

Question No. 2

Which of the following options is the closest in meaning to the sentence below?

She enjoyed herself immensely at the party

Question No. 3

Which one of the following combinations is incorrect?

Question No. 4

Based on the given statements, select the most appropriate option to solve the given question.

If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?

Statements:

(I) Each step is ¾ foot high.
(II) Each step is 1 foot wide.

Question No. 5

Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is probability that the sum of the two numbers equals 16?

Question No. 6

Select the alternative meaning of the underlined part of the sentence.

The chain snatchers took to their heels when the police party arrived.

Question No. 7

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option.
Statement:

There has been a significant drop in the water level in the lakes supplying water to the city.

Course of action:
(I)   The water supply authority should impose a partial cut in supply to tackle the situation.
(II)  The government should appeal to all the residents through mass media for minimal use of water.
(III) The government should ban the water supply in lower areas.

Question No. 8

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between numbers of female students in the Civil department and the female students in the Mechanical department?

Question No. 9

The probabilities that a student passes in Mathmatics, Physics and Chemistry are m,p, and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c:

(I)   p + m + c = 27/20
(II)  p + m + c = 13/20
(III) (p)$×$(m)$×$(c) = 1/10

Question No. 10

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

 Q No. Marks Answered Correctly Answered Wrongly Not  Attemted 1 2 21 17 6 2 3 15 27 2 3 1 11 29 4 4 2 23 18 3 5 5 31 12 1

What is the average of the marks obtained by the class in the examination?

Question No. 11

A random variable X has probability density function f(x) as given below:

If the expected value , then Pr$\left[X<0.5\right]$ is __________.

Question No. 12

If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?

Question No. 13

If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of determinant of the matrix is ________.

Question No. 14

Consider a function , where r is the distance from the origin and $\stackrel{^}{r}$ is the unit vector in the radial direction. The divergence of the function over a sphere of radius R, which includes the origin, is

Question No. 15

When the Wheatstone bridge shown is used to find value of resistance the Galvanometer G indicates zero current when ${R}_{1}=50\mathrm{\Omega }$, ${R}_{2}=65\mathrm{\Omega }$ and ${R}_{3}=100\mathrm{\mathrm{\Omega }}$. If is known with $±5%$ tolerance on its nominal value of 100$\mathrm{\Omega }$, what is tha range of ${R}_{X}$ in Ohms?

Question No. 16

A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0-500 A) is ________.

Question No. 17

Of the four characteristic given below, which are the major requirements for an instrumentation amplifier?
P. High common mode rejection ratio
Q. High input impedance
R. High linearity
S. High output impedance

Question No. 18

In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging current (in Ampere) of the 5 V battery, under steady-state, is ________.

A moving average function is given by $y\left(t\right)=\;\frac1T\int\limits_{t-T}^tu\left(\zeta\right)\operatorname d\zeta$. If the input u is a sinusoidal signal of frequency $\frac{1}{2T}\mathrm{Hz},$ then in steady state, the output y will lag u (in degree) by ________.