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QUESTION: 1

Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read _______ many of them

Solution:

Newspapers are a constant source of delight and recreation for me. The only (what bother’s) trouble is that I read too (a lot/ large) many of them.

QUESTION: 2

The missing number in the given sequence 343,1331,______, 4913 is

Solution:

343 = 73

1331 = 113

4913 = 173

All numbers given are cube of prime numbers so 133 = 2197 satisfy the missing number.

QUESTION: 3

The passengers were angry _______ the airline staff about the delay.

Solution:

The passengers were angry with the airline staff about the delay.

QUESTION: 4

It takes two hours for a person X to mow the lawn. Y can move the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to move the lawn?

Solution:

Time taken by X to now the lawn = 2 hrs.

∴ Work done by X in

Similarly, Work done by 4 in hr = ¼

Work done by x + 4 in 1 hr =

∴ Total time taken by X & 4 together =

= 80 Minutes

QUESTION: 5

I am not sure if the bus that has been booked will be able to ____ all the students.

Solution:

I am not sure if the bus that has been booked will be able to accommodate (occupy) all the students.

QUESTION: 6

Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of element having minimum and maximum values in the set Z is __________.

Solution:

Given that X = {1, 2, 3}

4 = {2, 3, 4}

Minimum value in

Maximum value in

QUESTION: 7

The ratio of the number of boys and girls who participated in an examination is 4 : 3. The total percentage of candidates who passed the examination is 80 and the percentage of girls who passed is 90. The percentage of boys who passed is __________

Solution:

Let number of boys participated = 4x Number of girls participated = 3x

Total number of students participated = 7x

Total passed candidates =

Girls candidate who passed =

Boys candidate who passed = Total passed candidate – Girls candidate who passed

QUESTION: 8

An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women feel more guilty about shopping.

Which one of the following statements can be inferred from the given text?

Solution:

The correct statement can be concluded from Venn diagram or using the Syllogism.

QUESTION: 9

How many integers are there between 100 and 1000 all of whose digits are even?

Solution:

For all digits of a number which lie between 100 and 1000 are even, Unit and tens digits can be filled from the set {0, 2, 4, 6, 8} But hundred’s digit does not include 0 as it will not remain a number which lie between 100 and 1000

∴ Hundreds digit set is {2, 4, 6, 8}

Total integer = 100 numbers

QUESTION: 10

Consider five people – Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1. Lakshmi is taller than Rekha

2. Rekha is shorter than Mita

3. Rekha is taller than Sana

4. Sana is shorter than Ganga

Solution:

Given that

Ganga > Rekha, Lakshmi

Lakshmi > Sana

Mita > Ganga

∴ Mita > Ganga > Rekha, Lakshmi > Sana

∴ 2 and statement 4 are correct

QUESTION: 11

The mean-square of a zero-mean random process is where k is Boltzmann’s constant, T is the absolute temperature, and C is capacitance. The standard deviation of the random process is

Solution:

Given that

Mean square of random process

Mean is given zero ⇒ E (x) = 0

We know that E(x^{2}) – [E(x)]^{2} = variance

Standard deviation =

QUESTION: 12

The characteristic equation of a linear timeinvariant (LTI) system is given by

∆(s) = s^{4} + 3s^{3} + 3s^{2} + s + k = 0.

The system is BIBO stable if

Solution:

Applying R.H criteria for stability

Δ(S) = S4 + 3S3 + 3S2 + S + K = 0

For stability, first column should be greater than zero

QUESTION: 13

The inverse Laplace transform of for ≥ 0 is

Solution:

H (t) = L^{–1} [H(S)]

H (t) = e^{–t}+2te^{–t}

QUESTION: 14

A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is

Solution:

We know that

Voltage Regulation =

Given that V_{FL} = 95V

V_{NL} = 100 V

QUESTION: 15

A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at power factor of 0.5 leading is

Solution:

We know that P = VI cos φ, as load and voltage are same

∴ I cos φ = constant

l_{1} cos φ_{1} = I_{2} cos φ_{2}

I_{1} = 200A

Cos φ_{1} = 1

Cos φ_{2} = 0.5

*Answer can only contain numeric values

QUESTION: 16

A cv-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity εr1 = 2. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity εr2, as shown to Figure (ii), the capacitance is doubled. The value of εr_{2} is _________.

Solution:

We know that

Total portion cover 2π

Both are connected in parallel

c_{2}= cr_{1}+ cr_{2
}

QUESTION: 17

The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is

Solution:

By reducing the rms value of supply voltage at rated frequency, magnetizing current changes which changes the magnetizing reactance

QUESTION: 18

The output response of a system is denoted as y(t), and its Laplace transform is given by

The steady state value of y(t) is

Solution:

For finding steady state value, we will apply final value theorem

QUESTION: 19

The open loop transfer function of a unity feedback system is given by

In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point

Solution:

Nyquist plot cut the negative real

Axis at w = phase cross over frequency

Magnitude at cutting point

Then, the co-ordinates becomes (-0.5, j0).

QUESTION: 20

A current controlled current source (CCCS) has an input impedance of 10 Ω and output impedance of 100 kΩ. When this CCCS is used in a negative feedback closed loop with a loop gain of 9, the closed loop output impedance is

Solution:

CCCS is current-shunt-negative feedback amplifier.

The output impedance R_{of}=R_{0}(1+βA),Given Aβ = 9

= 100 × 10^{3} (1 + 9)

= 1000 kΩ

QUESTION: 21

A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50 Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is

Solution:

We know that,

For 6-pulse converter harmonic present in AC current are 6K ± 1

General expression NK ± 1 [k = 0, 1, 2, 3]

For 6 pulse n = 6

Lowest order harmonic = 5

Lower harmonic frequency = 5 × 50 = 250 Hz

*Answer can only contain numeric values

QUESTION: 22

The current I flowing in the circuit shown below in amperes (round off to one decimal place) is ___________.

Solution:

Applying nodal analysis at point 1 whose voltage is assumed as V_{1}.

Solving (1) and (2)

8I = V_{1} – 6

8I = 20 – 2I – 6

10I = 14

I = 1.4 A

QUESTION: 23

The partial differential equation

Solution:

QUESTION: 24

Which one of the following function is analytic in the region |z| ≤ 1?

Solution:

the singularity z = –2 lies outside the |Z| < |

∴ By Cauchy’s integral theorem

*Answer can only contain numeric values

QUESTION: 25

If f = 2x^{3} + 3y^{2} + 4z, the value of line integral C grade f . dr evaluated over contour C formed by the segments (-3, -3, 2) → (2, -3, 2) → (2, 6, 2) → (1, 6, -1) is

Solution:

Given that

y = 2x^{3} + 3y^{2} + 4z

Applying the limits

*Answer can only contain numeric values

QUESTION: 26

Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is ___________.

Solution:

Net reactance of generator

Short Circuit MVA = I_{SC} ×Base MVA = 20 × 5 = 100 MVA

QUESTION: 27

Given V_{gs} is the gate-source voltage, V_{ds} is the drain voltage, and V_{th} is threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are

Solution:

For NMOS transistor to be in saturation the condition will be

V_{GS} > V_{th} And V_{DS} ≥ V_{GS} – V_{Th}

*Answer can only contain numeric values

QUESTION: 28

The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 Ω. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is ___________.

Solution:

I_{sec} = 5 × 20 = 100 A

V = I_{sec} R = 100 × 0.01 = 1V

VA output of CT = VI_{sec} = 100 × 1 100 VA

*Answer can only contain numeric values

QUESTION: 29

The Y_{bus} matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as

The magnitude of the series reactance of each line in pu (round off up to one decimal place) is ___________.

Solution:

Y_{12}= – (y_{12}) = – j20

Series admittance of each line =

Series reactance of each line =

*Answer can only contain numeric values

QUESTION: 30

The rank of the matrix, is__________.

Solution:

Determinant of M = |M|

|M| = 0 [0 – 1] – 1 [0 – 1] + 1 [1 – 0]

|M| = 2

|M| ≠ 0

∴ Rank of M = Number of Non zero rows in Echelon form

P (M) = 3

QUESTION: 31

The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

Solution:

H (t) = 1 + e^{–at} u (t)

QUESTION: 32

A system transfer function is If a_{1} = b_{1} = 0, and all other coefficients are positive, the transfer function represents a

Solution:

At s = 0

H (0) = constant

At s = ∞

∴ It is a low par filter

*Answer can only contain numeric values

QUESTION: 33

The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output voltage to be 75% of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ________.

Solution:

Waveform for output voltage of single phase full bridge PWM inverter

V_{o1rms} = fundamental r_{ms} output voltage

Given, V_{o1} = 0.754 V_{dc}

Pulse width = 2d = 112.88

QUESTION: 34

In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is

Solution:

For Maximum value of DC offset A

θ – φ = – 90

QUESTION: 35

M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M^{2} are

Solution:

M is a 2 × 2 Matrix with Eigen value 4 and 9 If has λ_{1}, λ_{2} _ _ _ _ _ λ_{n} Eigen values

M^{n} → λ_{1}^{n}, λ_{2}^{n} _ _ _ λ_{n}^{n} Eigen values

M^{2} → 4^{2}, 9^{2}

∴ M^{2} has Eigen values as 16 and 81

*Answer can only contain numeric values

QUESTION: 36

A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 μF/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end and energized with 400 kV at the sending end, the receiving end line voltage end line voltage in kV (round off to two decimal places) will be _____________.

Solution:

V_{S} = 400 KV

l = 300 km

L1 = 1 mH / km / phase

C1 = 0.01 μF / km / phase

*Answer can only contain numeric values

QUESTION: 37

The current I flowing in the circuit shown below in amperes is ______________.

Solution:

According to Mill man’s Theorem, the equivalent circuit of the given circuit is

E_{eq} = 0V

So, the current I flowing is 0 A

*Answer can only contain numeric values

QUESTION: 38

A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of (0.25 + j2.5) Ω/phase. The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is ____________.

Solution:

For synchronous motor

E_{g} = V_{1} – IZ

Z = (0.25 + j 2.5)Ω

I = 10 ∠ –36.86 A

Eg = 141.658 ∠–8.7 V (phase)

Eg = 245.36 V (line)

QUESTION: 39

The closed loop line integral

evaluated counter-clockwise, is

Solution:

*Answer can only contain numeric values

QUESTION: 40

The voltage across and the current through a load are expressed as follows

The average power in watts (round off to one decimal place) consumed by the load is _____________.

Solution:

P = 588.89 watts

*Answer can only contain numeric values

QUESTION: 41

A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator: R_{1} = 5.39 Ω, R_{2} = 5.72 Ω, X_{1} = X_{2} = 8.22 Ω. Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a 100 V (line), 10 Hz, three-phase AC source is __________.

Solution:

Given R_{1} = 5.39Ω, R_{2} = 5.72Ω, X_{1} = X_{2} = 8.22Ω for frequency → 10 Hz

Starting phase current at 10 Hz

I_{Pn} = 8.63A

Starting line current =

*Answer can only contain numeric values

QUESTION: 42

In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is 0.05 μF. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is _____________.

Solution:

Given data L = 50mH, C = 0.05 μF

Critical resistance to avoid current shopping will be given as

R = 500Ω

*Answer can only contain numeric values

QUESTION: 43

In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is ____________.

Solution:

QUESTION: 44

In the circuit below, the operational amplifier is ideal. If V_{1} = 10 mV and V_{2} = 50 mV, the output voltage (V_{out}) is

Solution:

QUESTION: 45

In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a

Solution:

The above expression is for XOR gate

*Answer can only contain numeric values

QUESTION: 46

A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is _________.

Solution:

Discharging of capacitor equation

VC (t) = Voe^{–t/τ}

Where τ = RC = (10^{3}) (10^{–7}) = 10^{–4} sec

V_{o} = 100V

V_{c}(t) = 100 e^{–104t}

V_{c}(t) = 1V

1 = 100 e^{–104t}

T = 0.46 msec

QUESTION: 47

A periodic function f(t), with a period of 2π, is represented as its Fourier series,

the Fourier series coefficients a1 and b1 of f(t) are

Solution:

*Answer can only contain numeric values

QUESTION: 48

If A = 2x**i** + 3y**j** + 4z**k** and u = x^{2} + y^{2} + z^{2}, then div (u**A**) at (1, 1, 1) is ________.

Solution:

div (UA) = (6x^{2} + 2y^{2} + 2z^{2}) + (3x^{2} + 9y^{2} + 3z^{2}) + (4x^{2} + 4y^{2} + 12z^{2})

at (1, 1, 1) ⇒ x = 1, y = 1, z = 1

div (UA) = 45

QUESTION: 49

A moving coil instrument having a resistance of 10 Ω, gives a full-scale deflection when the current is 10 m

Solution:

PMMC Instrument

I_{fs} = 10 mA

R_{m} = 10Ω

100 = I_{fs} (R_{m} + R_{se})

100 = 10 × 10^{–3} (10 + R_{sc})

R_{se} = 10000 – 10 = 9990Ω

QUESTION: 50

Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio ξ and the undamped natural frequency ωn (rad/sec) of the system are given by

Solution:

Comparing the above equation with the given problem

C = (1 0)

Characteristic equation is

|SI – A| = 0

s^{2} + 2Sβ + α = 0.........(1)

s^{2} + 2ξω_{n}s + ω_{n}^{2} = 0.............(2)

Comparing (1) and (2)

ω_{n}^{2} = α

QUESTION: 51

The enhancement type MOSFET in the circuit below operates according to the square law. μ_{n}C_{ox} = 100 μA/V^{2}, the threshold voltage (V_{T}) is 500 mV. Ignore channel length modulation. The output voltage V_{out} is

Solution:

QUESTION: 52

The asymptotic Bode magnitude plot of a minimum phase transfer function G(s) is shown below.

Consider the following two statements.

Statement I : Transfer function G(s) has three poles and one zero.

Statement II : At very high frequency (ω → ∞), the phase angle (jω)

Q. Which one of the following options is correct?

Solution:

From the given Bode plot,

T(S) = Transfer function =

It has three poles and no zero

So, statement 1 is false

∠T(s) = – 90 – tan^{–1} w – tan^{–1}

∠T(jw) |w → ∞ = – 270^{o}

So, statement 2 is true

*Answer can only contain numeric values

QUESTION: 53

A single-phase transformer of rating 25 kVA, supplies a 12 kW load at power factor of 0.6 lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is _____________.

Solution:

Load supplied previously before adding extra load 12 KW at pf of 0.6

S_{Load} = 12 + j16

Now, Let P be extra load added (Q_{extra} = as unity p.f)

S_{Load} = 12 + P + j16

Rated KVA |S_{rated}| = 25

So, 7.20 KW is extra load which is added

QUESTION: 54

Consider a 2 × 2 matrix M = [v1 v2], where. v_{1} and v_{2} are the column vectors. suppose where u_{1}^{T} and u_{2}^{T} are the row vectors. Consider the following statements :

Statement 1 :

Statement 2 :

Q. Which of the following options is correct?

Solution:

M^{–1} M = I

Statement 1 and 2 are both correct

*Answer can only contain numeric values

QUESTION: 55

A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is ___________.

Solution:

V_{sr} I_{sr} cos φ = V_{o}I_{o}

For single phase fully – controlled converter

I_{o} = I_{sr} = 10A

QUESTION: 56

A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of 24 Ω. The switching frequency of the converter is 250 Hz. If switch-on duration is 1 ms, the load power is

Solution:

Given that

Switch frequency, f_{s} = 250Hz

Load resistance R_{L} = 24Ω

Supply voltage V_{s} = 48V

T_{ON} = 1 msec

P = 6 watts

*Answer can only contain numeric values

QUESTION: 57

In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency is 50 kHz. Assume ideal components and a very large output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in μH) is ________.

Solution:

P_{o} = 120w, Vs = 24V, Vo = 48V

α = 0.5 [Duty cycle]

P_{o} = V_{o}I_{o} = 120

V_{S}I_{S} = V_{o}I_{o
}

At boundary of continuous & discontinuous

*Answer can only contain numeric values

QUESTION: 58

A 220 V DC shunt motor takes 3 A at noload. It draws 25 A when running at fullload at 1500 rpm. The armature and shunt resistances are 0.5 Ω and 220 Ω, respectively. The no-load speed in rpm (round off to two decimal places) is ________.

Solution:

No load

I_{NL} = 3A

I_{a} = I_{L} – I_{f} = 2A

Back cmf = Eb_{N} = V – I_{a}R_{a}

= 220 – 2 × 0.5 = 219V

Full load

I_{FL} = 25A N_{f} = 1500 rpm

I_{f} = 1A

I_{a} = I_{FL} – I_{f} = 24A

EbF = V – I_{a}R_{a} = 220 – 24 × 0.5 = 208 V

We know E α speed (N)

(N_{N} = speed at no load)

NN = 1579.33 rpm

*Answer can only contain numeric values

QUESTION: 59

A fully-controlled three-phase bridge converter is working from a 415 V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is ________.

Solution:

Ac line current rms = (I_{s})_{rms} =

QUESTION: 60

The output expression for the Karnuaugh map shown below is

Solution:

F (P, Q, R, S) =

*Answer can only contain numeric values

QUESTION: 61

The probability of a resistor being defective is 0.02. There are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is __________.

Solution:

P = 0.02

n = 50

λ = np = 50 (0.02) = 1

P (x ≥ 2) = 1 – P (x < 2)

= 1 – [P(x =0) + P (x = 1)]

P (x ≥ 2) = 1 – e^{–1} (1 + 1) = 0.26

*Answer can only contain numeric values

QUESTION: 62

The magnetic circuit shown below has uniform cross-sectional area and air gap of 0.2 cm. The mean path length of the core is 40 cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _________________.

Solution:

L_{air} = 0.2 cm

L_{m} = 40 cm

Given B_{o} = 1 Tesla at **µ _{r }**

L

Let a = uniform cross – sectional area

We know that

S

Case 1: when μr

Case 2:

Μ

MMF = Same

Put NI

B

*Answer can only contain numeric values

QUESTION: 63

A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ___________.

Solution:

Fault current for SLG fault

Fault current for 3φ fault

Xn = 0.1 Pu

X_{n} (inΩ) =

Xn (inΩ) = 1.8Ω

QUESTION: 64

The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120^{o} with respect to each other. The rms value of neutral current is

Solution:

QUESTION: 65

The transfer function of a phase lead compensator is given by

The frequency (in rad/sec), at which ∠D(jω) is maximum, is

Solution:

Frequency at which ∠T (jw) is maximum.......(i)

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