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This contains 65 Multiple Choice Questions for GATE Practice Test: Gate Electrical Engineering GATE 2015 Paper (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Q. No. 1 – 5 Carry One Mark Each

Which of the following combinations is incorrect?

Solution:

QUESTION: 2

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?

Solution:

Total number of pairs possible are 20(with 1 element from A and 1 element from B).The pairs which sum to 16 are 4nos, that are (2,14)(3,13)(4,12)(5,11) . So 4/20 =0.20

QUESTION: 3

Which of the following options is the closest in meaning to the sentence below? She enjoyed herself immensely at the party.

Solution:

QUESTION: 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.

Solution:

When we climb from one floor to other, it is the height that matters and not the width of the staircase.Therefore, From statement 1 only, we can figure out that 9 / (3/4) or 12 steps are required.

QUESTION: 5

Didn't you buy ________ when you went shopping?

Solution:

QUESTION: 6

Q. No. 6 – 10 Carry Two Marks Each

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.

Solution:

QUESTION: 7

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.

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

Solution:

*Answer can only contain numeric values

QUESTION: 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?

Solution:

QUESTION: 9

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

The chain snatchers "__took to their heels"__ when the police party arrived.

Solution:

QUESTION: 10

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

Solution:

*Answer can only contain numeric values

QUESTION: 11

A moving average function is given by f the input u is a sinusoidal signal of frequency then in steady state, the output y will lag u (in degree) by ________.

Solution:

*Answer can only contain numeric values

QUESTION: 12

Consider a one-turn rectangular loop of wire place in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B t 0.25sinωt, where 2π*50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 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 ________.

Solution:

QUESTION: 14

When the Wheatstone bridge shown is used to find value of resistance R_{x}, the Galvanometer G indicates zero current when R_{1}=50, R_{2=}65 & R_{3=}100. If R_{3} is known with __+__5% tolerance on its nominal value of 100, what is range of R_{x} in ohms?

Solution:

*Answer can only contain numeric values

QUESTION: 15

For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage, VTh (in volt), seen from terminal AB is _________.

Solution:

QUESTION: 16

The impulse response g(t) of a system, G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in Figure (b)?

Solution:

QUESTION: 17

Base load power plants are

P: wind farms.

Q: run-of-river plants.

R: nuclear power plants.

S: diesel power plants

Solution:

QUESTION: 18

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

Solution:

Additional characteristics include very low DC offset, low drift, low noise, very high open-loop gain, very high common-mode rejection ratio, and very high input impedances. Instrumentation amplifiers are used where great accuracy and stability of the circuit both short and long-term are required.

*Answer can only contain numeric values

QUESTION: 19

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

Solution:

QUESTION: 20

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

Solution:

QUESTION: 21

A separately excited DC generator has an armature resistance of 0.1Ω and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200 V. When this generator is operated at half the rated speed, with half the rated field current, an un-charged 1000 μF capacitor is suddenly connected across the armature terminals. Assume that the sped remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25 V?

Solution:

*Answer can only contain numeric values

QUESTION: 22

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 ________.

Solution:

QUESTION: 23

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?

Solution:

QUESTION: 24

The primary mmf is least affected by the secondary terminal conditions in a

Solution:

QUESTION: 25

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current, are given by: V_{1} =500 kV, V_{2} =485 kV and I=1.5 kA. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations id feasible?

If power is to be reversed

Solution:

QUESTION: 26

An inductor is connected in parallel with a capacitor as shown in the figure.

As the frequency of current i is increased, the impedance (Z) of the network varies as

Solution:

QUESTION: 27

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function

Solution:

QUESTION: 28

The voltages developed across the 3Ω and 2Ω resistors shown in the figure are 6V and 2V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5V voltage source?

Solution:

QUESTION: 29

The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?

Solution:

QUESTION: 30

A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

Solution:

QUESTION: 31

In the 4×1 multiplexer, the output F is given by . Find the required input 'I_{3} I_{2} I_{1} I_{0} '.

Solution:

*Answer can only contain numeric values

QUESTION: 32

A (0-50A) 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 (0-500A) is ________.

Solution:

QUESTION: 33

Consider the circuit shown in the figure,. In this circuit R=1k , and C=1μF. The input voltage is sinusoidal with a frequency of 50 Hz, represented as phasor with magnitude Vi and phase angle 0 radian as shown in the figure. The output voltage is represented as a phasor with magnitude V_{0} and phase angle δ radian. What is the value of output phase angle δ(in radian) relative to the phase angle of the input voltage?

Solution:

QUESTION: 34

A steady current I is flowing in the –x direction through each of two infinitely long wires as shown in the figure. The permeability of the medium is μ_{0}.

Solution:

H = H_{1}+H_{2}

QUESTION: 35

Consider a discrete time signal given by

x[n] = (-0.25)^{n} u[n]+ (0.5)^{n} u[-n -1]

The region of convergence of its Z-transform would be

Solution:

QUESTION: 36

Q. No. 36 – 65 Carry Two Marks Each

Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

Solution:

*Answer can only contain numeric values

QUESTION: 37

The circuit shown in meant to supply a resistive load R_{L} from two separate DC voltage sources. The switches S_{1} and S_{2} are controlled so that only one of them is ON at any instant. S_{1} is turned on for 0.2 ms and S_{2} is turned on for 0.3 ms in a 0.5 ms switching cycle time period. Assuming continuous conduction of the inductor current and negligible ripple on the capacitor voltage, the output voltage V_{0} (in Volt) across RL is ________.

Solution:

QUESTION: 38

Determine the correctness or otherwise of the following Assertion [a] and the Reason p[r]. Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions. Reason: Accuracy depends on the power mismatch vector tolerance.

Solution:

*Answer can only contain numeric values

QUESTION: 39

In the given circuit, the parameter k is positive, and the power dissipated in the 2 resistor is 12.5 W. The value of k is ________.

Solution:

QUESTION: 40

In the signal flow diagram given in the figure, u_{1} and u_{2} are possible inputs whereas y_{1} and y_{2} are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

Solution:

*Answer can only contain numeric values

QUESTION: 41

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5V is applied to Port1, a current of 1.25 A flows through a 1 resistance connected across Port 2. When 3V is applied to Port 1, then current (in Ampere) through a 2 resistance connected across Port 2 is _________.

Solution:

QUESTION: 42

A self commutating switch SW, operated at duty cycle δ is used to control the load voltage as shown in the figure.

Under steady state operating conditions, the average voltage across the inductor and the capacitor respectively, are

Solution:

*Answer can only contain numeric values

QUESTION: 43

The figure shown a digital circuit constructed using negative edge triggered J-K flip flops. Assume a starting state of Q_{2}Q_{1}Q_{0} =000. This state Q_{2}Q_{1}Q_{0} =000 will repeat after ________ number of cycles of the clock CLK.

Solution:

QUESTION: 44

The signum function is given by The Fourier series expansion of sgn(cos(t))has

Solution:

it represents square wave, which is even and half wave symmetry function, it contains cosine terms for all odd harmonics.

*Answer can only contain numeric values

QUESTION: 45

A DC motor has the following specifications: 10 hp, 37.5 A, 230V; flux/pole = 0.01 Wb, number of poles = 4, number of conductors = 666, number of parallel paths = 2. Armature resistance = 0.267Ω. The armature reaction is negligible and rotational losses are 600W. The motor operates from a 230V DC supply. If the motor runs at 1000 rpm, the output torque produced in (in Nm) is __________.

Solution:

QUESTION: 46

Find the transfer function Y(s)/ X(s) of the system given below.

Solution:

QUESTION: 47

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at (2-j3). List all the poles and zeroes

Solution:

*Answer can only contain numeric values

QUESTION: 48

Two single-phase transformers T_{1} and T_{2} each rated at 500 kVA are operated in parallel. Percentage impedances of T_{1} and T_{2} are (1+j6) and (0.8+j4.8), respectively. To share a load of 1000 kVA at 0.8 lagging power factor, the contribution of T2 (in kVA) is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 49

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is _______.

Solution:

QUESTION: 50

A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

Solution:

QUESTION: 51

The maximum value of “a” such that the matrix has three linearly independent real eigenvectors is

Solution:

Case (a) repeated roots (α,α,β)

Note that the graph of f(x) cannot be like the one given below

3real rootsnot possible

QUESTION: 52

The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?

Solution:

*Answer can only contain numeric values

QUESTION: 53

A 200/400V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rating 200/600V. A resistive load of 12 is connected to the high voltage (600V) side of the auto-transformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 54

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below:

The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is _____.

Solution:

QUESTION: 55

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of p will the magnitude of V_{0} be maximum?

Solution:

*Answer can only contain numeric values

QUESTION: 56

A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200V DC source and the rated voltage is applied to the field winding. The armature resistance of this motor is 1. The no-load armature current is negligible. With the motor developing its full load torque, the armature voltage is set so that the rotor speed is 500 rpm. When the load torque is reduced to 50% of the full load value under the same armature voltage conditions, the speed rises to 520 rpm. Neglecting the rotational losses, the full load armature current (in Ampere) is _______.

Solution:

*Answer can only contain numeric values

QUESTION: 57

A solution of the ordinary differential equation is such that y(0) = 2 and The value of is ___________.

Solution:

QUESTION: 58

The op-amp shown in the figure has a finite gain A = 1000 and an infinite input resistance. A step-voltage V_{i} = 1 mV is applied at the input at time t = 0 as shown. Assuming that the operational amplifier is not saturated, the time constant (in millisecond) of the output voltage V_{0} is

Solution:

*Answer can only contain numeric values

QUESTION: 59

A 3-phase 50 Hz square wave (6-step) VSI feeds a 3-phase, 4 pole induction motor. The VSI line voltage has a dominant 5^{th} harmonic component. If the operating slip of the motor with respect to fundamental component voltage is 0.04, the slip of the motor with respect to 5^{th} harmonic component of voltage is ________.

Solution:

QUESTION: 60

An 8 bit unipolar Successive Approximation Register type ADC is used to convert 3.5V to digital equal output. The reference voltage is +5V. The output of ADC at end of 3^{rd }clock pulse after the start of conversion is ________.

Solution:

The block diagram of SAR type ADC is as follows

Unipolar means all the voltages will be +ve i.e. nothing is –ve. The functionality of SAR type DAC is, it will load a value to output register with MSB=1 and remaining bit=0, and it will cross check a logic as follows.

*Answer can only contain numeric values

QUESTION: 61

The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of 50 Hz. It uses unipolar pulse width modulation with switching frequency of 50 kHz and modulation index of 0.7. For V_{m} = 100 V DC, L = 9.55 mH, C = 63.66 μF, and R = 5, the amplitude of the fundamental component in the output voltage V0 (in volt) under steady-state is __________.

Solution:

QUESTION: 62

f(A,B,C,D) = Πm (0,1,3,4,5,7,9,11,12,13,14,15) is a maxterm representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is

Solution:

*Answer can only contain numeric values

QUESTION: 63

A 50Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle δ is 5°, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of δ in degrees, 0.02 second after the fault is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 64

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by v(t) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

Solution:

*Answer can only contain numeric values

QUESTION: 65

In the given circuit, the silicon transistor has β= 75 and collector voltage V_{c =}9V. Then the ratio of R_{B} and R_{C} is _______.

Solution:

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