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This mock test of Electrical Engineering (EE) : Mock Test 3 For GATE for GATE helps you for every GATE entrance exam.
This contains 65 Multiple Choice Questions for GATE Electrical Engineering (EE) : Mock Test 3 For GATE (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Choose the word or phrase which is nearest in meaning to the key word Lethargy

Solution:

QUESTION: 2

Break : Piece

Solution:

QUESTION: 3

Replace the phrase printed in bold to make it grammatically correct ?

** "Even though many companies"** are now penetrating rural India, it would help to give India a real chance of witnessing a double digit GDP growth.

Solution:

QUESTION: 4

Improve the sentence with suitable options by replacing the underlined word.

He is still in vigorous health although he is on the **" right"** side of sixty.

Solution:

QUESTION: 5

Complete the given sentence by choosing the correct phrase.

You cannot succeed unless ________

Solution:

QUESTION: 6

Chirag decided to give 12% of his salary to his younger brother as a pocket money. But he gave 1260 Rs which was 60% of what he had decided earlier. How much is Chiragâ€™s salary?

Solution:

Let x be Chiragâ€™s salary:

(0.12x) X 0.6 = 1260

x = 17500 Rs

QUESTION: 7

Two pipes can fill a tank in 15 minutes and 25 minutes respectively. Both the pipes are opened together and after some time, the first pipe is closed and the tank is completely full in 15 minutes. For how many minutes is the first pipe opened?

Solution:

t = 6 minutes

QUESTION: 8

A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that at least one of them solves the problem.

Solution:

Probability that at least one of them solves the problem = P

P = 1 â€“ 1/2 X 2/3 = 2/3

QUESTION: 9

What is the probability that a leap year has 53 Sundays and 52 Mondays?

Solution:

In leap year there are 366 days.

There are 52 weeks + 2 days

1. - Mon. + Tue.

2. - Tue. + Wed.

3. - Wed. + Thu.

4. - Thu. + Fri.

5. - Fri. + Sat.

6. - Sat. + Sun. ? 53 Sundays + 52 Mondays

7. - Sun. + Mon.

Probability = 1/7

QUESTION: 10

A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?

Solution:
Let be the rate of interest:

r = 12% per annum

QUESTION: 11

When a lead-acid battery is in fully charged condition, the colour of its positive plate is

Solution:

QUESTION: 12

Determine the value of load resistance ,so that it receive maximum power from the circuit.

Solution:

QUESTION: 13

A plant has the following transfer function, , For an unit step input determine the time required so that response will settle in 2% of its final value.

Solution:

QUESTION: 14

The open loop transfer function of an unity feedback control system is G(S) = ,What is the range of K so that closed loop system becomes stable ?

Solution:
Characteristics equation

= K S(S 1) (S 5) = 0

Rough-array

So for stable system K > 0

and

30 â€“ k > 0

k < 30

so 0 < k < 30

= K S(S 1) (S 5) = 0

Rough-array

So for stable system K > 0

and

30 â€“ k > 0

k < 30

so 0 < k < 30

QUESTION: 15

Determine the peak inverse voltage that appear across the diode in the given circuit.

Solution:

During positive half cycle capacitor get charge and during negative half cycle the equivalent circuit is shown as

so, V_{D} = V_{m}Sinωt

so, P1V = 2V_{m}

here, V_{m} = 10 volt,

so, P1V = 20 volt

QUESTION: 16

Determine the power dissipated across the load resistance R_{L} in the given circuit, assume diode is ideal.

Solution:

Power dissipate across R_{L},

here, V_{rms} = 5/2

so,

= 125 mW

QUESTION: 17

What is the load current I_{L} in the circuit shown below:

Solution:

Apply KCL at node V_{1},

…..(1)

Apply KCL at node V_{2},

…..(2)

From equation (1) and (2)

Therefore,

= – 10mA

QUESTION: 18

How many standard resistor are required to design a 3 bit flash type ADC?

Solution:

Number of resistor, = 2^{n}

= 2^{3}

= 8

QUESTION: 19

Determine the size of ROM required to implement a full-substractor.

Solution:

For full-substractor, the number of input variable is 3 and output function are 2

So size of ROM,

2^{3} × 2

8 × 2

QUESTION: 20

Determine the even part of the signal x(f) where x(t) = 4 Sin t

Solution:

x(t) = 4 sint

Since the above signal is an odd signal therefore, its even part is zero.

QUESTION: 21

An LTI system is characterized by difference equation **y (n) = y (n-1) x (n)**. The impulse response of the system is :

Solution:

y(n) = y(n – 1) x(n)

⇒

QUESTION: 22

Consider the signal x(t) = e^{-2t} u(t). Let X(Ï‰) denotes the Fourier transform of the signal, the value of the below equation is:

Solution:

Since, ,

So,

Therefore

= 2Ï€

QUESTION: 23

In the given circuit, the forward threshold voltage of the diode is 0.

Solution:

Given P_{Dmax} = 21 mW

So, I_{Dmax} = 21mW/0.7 = 30mA

For same operation,

50 â€“ 0.7 <= 30 R

19.3 <= 30 R

R >= 643

So, only option (b) is satisfied.

QUESTION: 24

When a bypass capacitor is connected across the emitter and resistance of a common-emitter BJT amplifier:

Solution:

QUESTION: 25

An amplifier using an op-amp with a slew rate 1 V/μsec has a gain of 20 dB. If the peak value of sinusoidal input signal is 1 V then determine the maximum frequency of the input signal that can be amplify without any distortion.

Solution:

For distortion less output,

2p f_{m} A_{f} V_{m} <= S.R

Here, A_{f} = 20dB

i.e, A_{f }= 10

So,

QUESTION: 26

The skin depth of copper at a frequency of 6GHz is 1μm, the skin depth at a frequency of 24 GHz would be :

Solution:

Skin Depth, δ =

QUESTION: 27

If the current changes from 5A to 3A in 2 seconds and the inductance is 10H, calculate the emf.

Solution:

We know that:

emf=L(i2-i1)/t

Substituting the values from the question, we get emf=10V.

QUESTION: 28

What is the capacitance when *Q* = 60 C and *V* = 12 V?

Solution:

QUESTION: 29

The surge impedance of a 400 KV, 100 Km T-line is 300for a 200 Km length, the surge impedance will be.

Solution:

Because surge impedance of a T-line is independent on line length and frequency

QUESTION: 30

The dielectric loss of a capacitor can be measured by which one of the following :

Solution:

QUESTION: 31

The value of the below integral is equal to

Solution:

QUESTION: 32

Evaluate, , where C represents a circle

Solution:

,

Since pole z = 4 lies within the circe. So,

QUESTION: 33

From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friends for picnic. If there have to be exactly 3 girls in invites, then the number of ways in which he can invite them are,

Solution:

Three girls can be selected from 5 girls in ^{5}C_{3 }ways. As number of boys to be invited is not given, hence out of 4 boys he can invite them in 2^{4} ways, so total of

2^{4} X ^{5}C_{3 }ways = 16 X =160 ways

QUESTION: 34

A dice is rolled 5 times. The probability that 4 will show up exactly 3 times is:

Solution:

Probability of getting four is,

P(4) = 1/6

So, Required Probability,

QUESTION: 35

Consider a vector A given by :

Solution:

QUESTION: 36

Determine V_{0} in the given circuit below

Solution:

5V_{1 }= 20

V_{1} = 4 volt,

So, V_{0} = -V_{1}

_{ }= -4 volt

QUESTION: 37

The Y-parameter of the circuit shown below :

Solution:

Compare with standard π network,

QUESTION: 38

In the circuit shown below, the switch is closed at t=0, determine

Solution:

At t = 0^{ } the equivalent circuit is,

QUESTION: 39

A voltage commutated chopper circuit operated at 500Hz is shown below. Find circuit turn-off time of main SCR and Aux-SCR

Solution:

Circuit turn-off time of

QUESTION: 40

The value of δ(t) * 2δ(t-1) * 3δ(t-2) is

Solution:

δ(t) * 2δ(t-1) * 3δ(t-2)

δ(t) * 6δ(t-3)

6δ(t-3)

QUESTION: 41

The ROC of z transform of signal x[n] = (4)^{|n|} is

Solution:

x(n) = 4^{|n|}

=

So,

ROC > 4 & ROC < 1/4

Since there is no any common ROC so, z-transform does not exist.

QUESTION: 42

The system matrix of a continuous time system is described in the state variable form is,

The system is stable for

Solution:

Matrix,

Characteristic equation,

For a stable system, all the elements in the first column of Routh-array should be positive. In the given option, option (c) satisfy the criteria i.e., A < 0 and B < 1/2

QUESTION: 43

The resin bonded paper bushings are designed to operate at a maximum radial stress of

Solution:

QUESTION: 44

The open-loop transfer function of unity feedback control system is

.

The system is stable for

Solution:

Characteristic equation

QUESTION: 45

In the given logic diagram the propagation delays of both the gates are 20 nsec each. The output y is at logic ‘1’ from a long time and at t = 0, the input x change from 0 to 1, so the output goes momentary to logic 0, determine the time required by the output to again maintain its level at logic 1.

Solution:

So output again becomes 1 after 40 nsec.

QUESTION: 46

The logical expression realized by the circuit shown in the figure will be:

Solution:

QUESTION: 47

In the circuit A = 1, B = 1, Q_{n} = 0 and P_{n} = 1 what will be the output Q_{n 1} and P_{n 1} when the clock input (CK) is applied ?

Solution:

QUESTION: 48

For what value of damping parameter, the transient stability is assured by equal area criterion?

Solution:

Equal area criterion is applicable only if damping is zero.

QUESTION: 49

The current through the resistor R in the given circuit.

Solution:

V_{1} = 2volt {Due to virtual short – circuit}

and

Since β is not given take it to be very large, iem

I_{E } = I_{c} = 10 mA

QUESTION: 50

Determine the operating point of the BJT, in the given circuit.

Solution:

V_{B} = 5 volt,

So, V_{E} = 5 â€“ 0.7 = 4.3

I_{E} = mA = 1.075 mA

Now, V_{C} = 10 â€“ 2 * I_{C}

= 10 â€“ 2*1.075

= 7.85V

So, V_{CE} = V_{C} â€“ V_{E}

= 7.85 â€“ 4.3

= 3.55 V

QUESTION: 51

In the circuit shown in the given figure, assume that the capacitor C is almost shorted for the frequency range of interest of the input signal. Under this condition, the voltage gain of the amplifier will be approximately.

Given h_{fe} = 100 & h_{ie} = 1K

Solution:

It is common collector configuration (emitter follower) so voltage gain is almost equal to 1, in the given option A_{v} ≈ 1

QUESTION: 52

For a Si transistor connected as shown in the fig. V_{BE} = 0.7V. Given that the reverse saturation current of the junction at room temperature is 200 nA, the I_{C} is given by

Solution:

Since base is connected to collector of the transistor, therefore it works as a diode

I_{c} = I_{0}{e^{VBE/ηVT}-1}

Here, I_{0} = 200 nA, V_{BE} = 0.7, η = 2, V_{T} = 26 mV

So, I_{c} = 147.86 mA

QUESTION: 53

A 220 KV, three phase transmission line is 40 Km long. The resistance per phase is 0.15per Km and inductance per phase is 1.5923 mH per Km. The line is supplying a 3 phase load of 381 MVA at 0.8 power factor lagging. Find voltage at sending end will be (per phase)

Solution:

Resistance of the line per phase for a length of 40 Km.

R = 0.15 X 40 = 6 Ohm

Similarly reactance of the line (40 Km) per phase.

X_{L} = 11.5293 X 40 = 63.69 mH

Receiving and voltage / phase

Load power factor = 0.8 lagging

I = =1000 Amp

Sending end voltage,

V_{S} = V_{r } IR cosÏ† IX_{L}sinÏ†

= 127 x 10^{3} 1000 x 6 x 0.8 1000 x 63.69 x 10^{-3} x 0.6

= 170 KV

QUESTION: 54

Magnetic flux density in certain medium with permeability μ_{r} is given by . The current density is given by

Solution:

The current density,

QUESTION: 55

Given field, Â = 3x^{2}yzâ_{x} x^{3}zâ_{y} (x^{3}y - 2z)â_{z} It can be said that A is

Solution:

Â = 3x^{2}yzâ_{x} x^{3}zâ_{y} (x^{3}y - 2z)â_{z}

So the given field is conservative

QUESTION: 56

A synchronous motor with negligible armature resistance at a load angle of 20° at rated frequency. If supply frequency is increased by 10% keeping other parameters constant the new load angle will be?

Solution:

QUESTION: 57

A variable speed drive rated for 1500 rpm, 40Nm, is reversing under no-load. Figure shows the reversing torque and the speed during the transient. The moment of inertia of the drive is……….

Solution:

QUESTION: 58

A (0-300)V Voltmeter has a guaranteed accuracy of 2% of full scale reading if the voltage measured by this instrument is 180V then the limiting error will be

Solution:

Error = 2% of F.S.D.

= 2% of 300 V

= 2/100 x 300 = 6 V

Measured Value = 180 V

Error = 6 V

Absolute error = Measured value – True value

6 = 180 - True value

Tue Value = 174 Volt

Limiting error or % error

= 6/174 x 100 = 3.44%

QUESTION: 59

A fault current of 2000A is passing on the primary side of 400/5 CT on the secondary side of the C.T. an inverse time over current relay is connected whose plug setting is set at 50%. The PSM will be

Solution:

The pickup value of the relay is 5A, since the relay setting is 50%

Therefore, The operating current of the relay is

5 x 50/100 = 2.5 A

QUESTION: 60

If the voltage across the units in a 2-unit suspension insulator is 60% and 40% respectively, of the line voltage. Determine the ratio of the capacitance of the insulator to that of its capacitance to earth.

Solution:

From figure I = I_{1} I'_{1}

V_{2}wkc = V_{1}wkc V_{1}wc

V_{2}wkc = V_{1}wc (k 1)

0.6 Vkwc = 0.4 Vwc (k 1)

â‡’ K = 2

QUESTION: 61

A salient pole synchronous motor is running with normal excitation it the excitation is reduced to zero than?

Solution:

because torque developed T = T_{Rl} T_{elect}

If ext^{n} zero electromagnetic zero by reluctance torque present incase of salient pole so it becomes reluctance motor.

QUESTION: 62

Given a > 0, we wish to calculate the reciprocal value 1/a by Newton â€“ Raphson method for f(x)=0 for a=7 and starting with X_{0} = 0.2, the first two iterations would be :

Solution:

Here, Let

â‡’

Therefore,

After Simplification,

For a = 7

Here x_{0} = 0.2

So x_{1} = 2 x 0.2 - 7 (0.2)^{2}

= 0.12

and second iteration

x_{2} = 2x_{1} - 7x_{1}^{2}

= 2 x 0.12 - 7 (0.2)^{2}

x_{2} = 0.1392

QUESTION: 63

For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 __NOT__ have a unique solution?

Solution:

QUESTION: 64

Cayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix below. Find A^{8}:

Solution:

Characteristic equation, - λ (3-λ) 2 = 0

λ^{2 }- 3λ 2 = 0

So, A^{2 }- 3A 2I = 0 .....(1)

⇒ New, A^{4 }= A^{2} x A^{2}

From equation (1),

A^{4 } = (3A – 2I) × (3A – 2I)

= 9A^{2} – 12A 4I

= 9{3A – 2I} – 12A 4I

= 27A – 18I – 12A 4I

A^{4} = 15 A – 14I

Now, A^{8} = A^{4} × A^{4}

= (15A – 14I) × (15A – 14I)

= 225 A^{2} – 420 A 196I

= 225 {3A – 2I} – 420 A 196I

A^{8} = 255 A – 254 I

QUESTION: 65

f(x) = 2x^{3} - 15x^{2} + 36x + 1 is increasing in the interval given below, choose the correct option.

Solution:

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