# Electrical Engineering - GATE 2015 Paper Solution

#### SET - 1

Didn’t you buy _________ when you went shopping?

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

She enjoyed herself immensely at the party

Which one of the following combinations is incorrect?

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.

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?

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

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

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.

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? 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

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?

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

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

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

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 ________.

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

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 the range of ${R}_{X}$ in Ohms? 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 ________.

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

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 $\style{font-family:'Times New Roman'}{y\left(t\right)=\;\frac1t\int_{t-T}^tu\left(\tau\right)}$. 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 ________. 