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QUESTION: 1

Q. 1 – Q. 5 carry One mark each.

The man who is now Municipal Commissioner worked as ___________

Solution:

Option (A) and (D) cannot be the answers because of the word ‘the security’

QUESTION: 2

Nobody knows how the Indian cricket team is going to "__cope with"__ the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

Solution:

**put up with** - is a phrasal verb

Meaning : to accept somebody/something that is annoying, unpleasant without complaining

QUESTION: 3

Find the odd one in the following group of words.

mock, deride , praise, jeer

Solution:

‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’

QUESTION: 4

Pick the odd one from the following options.

Solution:

In options A, B and C, the letters skipped between consecutive pair of letters in the English alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are present instead of M and N so, option ‘D’ is odd one from the group.

QUESTION: 5

In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of

Solution:

QUESTION: 6

Q. 06 – Q. 10 carry two marks each.

Among 150 faculty members in an institute, 55 are connected with each other through Facebook^{® }and 85 are connected through WhatsApp^{®}. 30 faculty members do not have Facebook^{® }or WhatsApp^{®} accounts. The number of faculty members connected only through Facebook^{® }accounts is _________

Solution:

Total faculty members = 150

The faculty members having facebook account = FB = 55

The faculty members having whatsapp = W = 85

The faculty members do not have face book (or) Whats App accounts = 30

The faculty members having any account = 150 - 30 = 120

The faculty members having both the accounts = (FB + W) - 120 = (55 + 85) - 120 = 20

The number of faculty members connected only through Facebook accounts = 55 - 20 = 35

QUESTION: 7

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.

Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.

(ii) Mobile computers and the internet are both intended inventions.

Solution:

The first and second sentences tell us that computers are invented for computation and internet for intended invention. These sentences lead to option ii so option (B) is the right inference

QUESTION: 8

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty in not a hill-station.

(ii) No hill-station can have more than one lake.

Solution:

Statement (i) is not true because Ooty is a hill station due Ooty has two lakes statement(ii) is also not true, because in given statements, for hill station one lake is compulsory but not mentioned about number of lakes.

QUESTION: 9

In a 2*4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

Solution:

In given 2*4 rectangle grid, the following type of rectangles are present.

One figured rectangles = 8

Two figured rectangles = 10

Three figured rectangles = 4

Four figured rectangles = 5

Six figured rectangles = 2

Eight figured rectangles = 1

Total No. of rectangles = 30

The No. of rectangles observed in the given grid = 30.

QUESTION: 10

Choose the correct expression for f(x) given in the graph.

Solution:

@ x = 3 from given graph f(x) must be equals to zero

QUESTION: 11

Q. 11 – Q. 35 carry One mark each.

The maximum value attained by the function f(x) = x(x –1) (x –2) in the interval [1, 2] is _______

Solution:

QUESTION: 12

Number of parallel path in wave winding is:

Solution:

QUESTION: 13

The Laplace Transform of f(t) = e^{2t} sin(5t) u(t) is

Solution:

QUESTION: 14

A function y(t), such that y(0) = 1 and y(1) = 3e^{–1}, is a solution of the differential equation

Then y(2) is

Solution:

QUESTION: 15

The value of the integral over the contour |z| = 1, taken in the anticlockwise direction, would be

Solution:

QUESTION: 16

The transfer function of a system is The steady state output y(t) is Acos(2t+) for the input cos(2t). The values of A and , respectively are

Solution:

QUESTION: 17

The phase cross-over frequency of the transfer function G(s) 100/(s+1)^{3} in rad /s is

Solution:

QUESTION: 18

Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) cos(t)

This system is

Solution:

given y(t) = x(t) cos(t)

It satisfies both additivity and Homogentity principles, so it is linear

If the input is delayed by t_{0}

QUESTION: 19

The value of where δ(t) is the Dirac delta function is

Solution:

QUESTION: 20

A temperature in the range of –40°C to 55°C is to be measured with a resolution of 0.1°C. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is

Solution:

The minimum ‘n’ value which can satisfy the above equation is 10

The minimum number of bits are 10

QUESTION: 21

Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output F in terms of A and B is

Solution:

QUESTION: 22

A transistor circuit is given below. The Zener diode breakdown voltage is 5.3 V as shown. Take base to emitter voltage drop to be 0.6 V. The value of the current gain β is __________.

Solution:

Zener diode is in breakdown, replace it with a voltage source of value V_{2} = 5.3 V & V_{BE} = 0. 6 V

QUESTION: 23

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by = f(r, z), where f is a continuous function of r and z. Let be the resulting electric field. Then the magnitude of

Solution:

A uniformly charged ring is specified. It can be considered as static. A static electric charge produces an electric field for which =0 .

QUESTION: 24

The power factor of pure resistive circuit is

Solution:

QUESTION: 25

RA and RB are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the statements is TRUE?

Solution:

QUESTION: 26

In a constant V/f induction motor drive, the slip at the maximum torque

Solution:

In an induction motor operating at any voltage V_{r}, frequency f, slip for max torque = r_{2} / x_{2} where x_{2} = 2πL_{2} f.

Now; if frequency is changed (irrespective of whether v/f is constant or not) x_{2} changes proportionally. So slip for maximum torque is inversely proportional to frequency. Synchronous speed is directly proportional to frequency. Hence slip of maximum torque has an inverse relation with synchronous speed.

*Answer can only contain numeric values

QUESTION: 27

In the portion of a circuit shown, if the heat generated in 5 resistance is 10 calories per second then heat generated by the 4? resistance, in calories per second, is _________

Solution:

*Answer can only contain numeric values

QUESTION: 28

In the given circuit, the current supplied by the battery, in ampere, is ________.

Solution:

QUESTION: 29

In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iteration.

Solution:

Total No. of buses = 100

Generator bus = 10 -1 = 9

Load busses = 90

Slack bus = 1

If 2 buses are converted to PQ from PV it will add 2 unknown voltages to iteration but unknown angles remains constant.

*Answer can only contain numeric values

QUESTION: 30

The magnitude of three-phase fault currents at buses A and B power system are 10 pu and 8 pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at bus B in pu, is ________.

Solution:

QUESTION: 31

Consider a system consisting of a synchronous generator working at a lagging power factor, a synchronous motor working at an overexcited condition and a directly grid-connected induction generator. Consider capacitive VAr to be a source and inductive VAr to be a sink of reactive power.

Which one of the following statements is TRUE?

Solution:

Sync. Generator with lagging PF ⇒ supply P & Q

Sync. Motor with over excitation ⇒ supply Q

Induction motor ⇒ Absorbs Q

*Answer can only contain numeric values

QUESTION: 32

A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage VL during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is _________.

Solution:

In steady state, area of inductor voltage for one switching cycle is zero

*Answer can only contain numeric values

QUESTION: 33

A steady dc current of 100 A is flowing through a power module (S, D) as shown in Figure (a). The V-I characteristics of the IGBT (S) and the diode (D) are shown in Figure (b) and (c), respectively. The conduction power loss in the power module (S, D) in watts, is ________.

Solution:

No current flows through the IGBT. So current flows only in Diode

Conduction loss

QUESTION: 34

A 4-pole, lap-connected separately excited dc motor is drawing a steady current of 40 A while running at 600 rpm. A good approximation for the waveshape of the current in an armature conductor of the motor is given by

Solution:

With lap winding, and 4 poles, number of parallel paths = 4, with a total armature current of 40 A; current in each path and hence current in each armature conductor is 10 A. It remains constant at 10 A as long as the conductor is in one path. When it goes into the next path (due to commutator action) the current in it reverses and becomes – 10 A. Assuming straight line commutation, the change from (+ 10 A) to (–10 A) is linear. With 600 RPM; time for 1 revolution = 0.1 sec. Time of a conductor to cover 1 pole-pitch= 0.1/4 = 25 ms. This is the width of one half cycle of conductor current.

QUESTION: 35

If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the equivalent inductance at port 1 is

Solution:

An inductance of L H in the low voltage side becomes n^{2}L H referred to the high voltage side (hv turns/ lv turns = n).

*Answer can only contain numeric values

QUESTION: 36

Q. 36 – Q. 65 carry Two marks each.

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 37

Let The value of α in the range 0 < α < 1, such that S = 2α is

Solution:

QUESTION: 38

Let the eigenvalues of a 2×2 matrix A be 1, -2 with eigenvectors x_{1} and x_{2} repsectively. Then the eigenvalues and eigenvectors of the matrix A^{2}-3A+4I would respectively, be

Solution:

QUESTION: 39

Let A be a 4×3 real matrix which rank2. Which one of the following statement is TRUE?

Solution:

QUESTION: 40

Consider the following asymptotic Bode magnitude plot (ω is in rad/s)

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

Solution:

From the given Bode plot the corner frequencies are 2 rad/sec and 4 rad/sec

*Answer can only contain numeric values

QUESTION: 41

Consider the following state - space representation of a linear time-invariant system.

The value of y(t) for t = log_{e}2 is ___________.

Solution:

QUESTION: 42

Loop transfer function of a feedback system is G(s)H(s) = Take the Nyquist contour in the clockwise direction. Then the Nyquist plot of G(s) encircles -1 + j0

Solution:

*Answer can only contain numeric values

QUESTION: 43

Given the following polynomial equation s^{3} + 5.5s^{2} + 8.5s + 3 = 0 the number of roots of the polynomial which have real parts strictly less than -1 is __________.

Solution:

Two roots real parts are less than -1

QUESTION: 44

Suppose x_{1}(t) and x_{2}(t) have the Fourier transforms as shown below

Which one of the following statements is TRUE?

Solution:

QUESTION: 45

The output of a continuous-time linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal A signal z(t) is called eigen-signal of the system T, when T{z(t)} = yz(t), where γ is a complex number, in general and is called an eigenvalue of T. Suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?

Solution:

QUESTION: 46

The current state Q_{A}Q_{B} of a two JK flip-flop system is 00. Assume that the clock rise-time is much smaller than the delay of the JK flip-flop. The next state of the system is

Solution:

The next state of the system Q_{A} Q_{B} = 11

QUESTION: 47

A 2-bit flash Analog to Digital Converter (ADC) is given below. The input is 0≤V_{N}≤3 Volts. The expression for the LSB of the output B_{o} as a Boolean function of X_{2}, X_{1} and X_{0} is

Solution:

QUESTION: 48

Two electric charges q and -2q are placed at (0, 0) and (6, 0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

Solution:

*Answer can only contain numeric values

QUESTION: 49

In the circuit shown, switch S_{2} has been closed for a long time. At time t = 0 switch S_{1} is closed. At t = 0^{+}, the rate of change of current through the inductor, in amperes per second, is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 50

A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.

Solution:

Initial load = (800 + j600)

load after modification = (900 + j600) to maintain same heat dissipation magnitude of power should be same

Load with compensation = (900 + j 600 + Compensation) = 900 + jx)

Equating magnitude of power= 800^{2} + 600^{2} = 900^{2} + x^{2}

Reactive power to be compensated by capacitor to achieve this is 164.11 kVAr

*Answer can only contain numeric values

QUESTION: 51

A 30 MVA 3-phase, 50Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance (Xn) is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of X_{n} (in p.u) that will limit the positive sequence current to 4270 A is _____________.

Solution:

QUESTION: 52

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then

Solution:

QUESTION: 53

A single-phase thyristor-bridge rectifier is fed from a 230 V, 50Hz single-phase AC mains. If it is delivering a constant DC current of 10A, at firing angle of 30°, then value of the power factor at AC mains is

Solution:

Power factor at input mains

*Answer can only contain numeric values

QUESTION: 54

The switches T1 and T2 in Figure are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage v_{m}(t) = 0.8sin(200ωt) V and the triangular carrier (V_{c}), voltage (v_{C}) are as shown in figure (b). The carrier frequency is 5 kHz. The peak value of the 100 Hz component of the load current (i_{L}) in Ampere, is ____________.

Solution:

*Answer can only contain numeric values

QUESTION: 55

The voltage (v_{s}) across the current (i_{s}) through a semiconductor switch during a turn-ON transition are shown in figure. The energy dissipated during the turn-ON transition, in mJ, is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 56

A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the rated condition. When operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz the value of the hysteresis loss divided by the eddy current loss is __________.

Solution:

If v/f is kept constant, maximum core flux density is constant.

In the problem, (400/50) = (200/25) = 8 (416/52). v/f is kept constant. So the maximum core flux density is constant. Let it be B.

*Answer can only contain numeric values

QUESTION: 57

A DC shunt generator delivers 45 A at a terminal voltage of 220 V. The armature and the shunt field resistances are 0.01 Ω and 44 Ω respectively. The stray losses are 375 W. The percentage efficiency of the DC generator is __________.

Solution:

*Answer can only contain numeric values

QUESTION: 58

A three-phase, 50Hz salient-pole synchronous motor has a per-phase direct-axis reactance (X_{d}) of 0.8 pu and a per phase quadrature-axis reactance (X_{q}) of 0.6pu. Resistance of the machine is negligible. It is drawing full-load current at 0.8 pf (leading). When the terminal voltage is 1pu, perphase induced voltage, in pu, is __________.

Solution:

QUESTION: 59

A single-phase 22kVA, 2200 V/220 V, 50 Hz, distribution transformer is to be connected as an auto transformer to get an output voltage of 2420 V. Its maximum kVA rating as an autotransformer is

Solution:

QUESTION: 60

A single-phase full-bridge voltage source inverter (VSI) is fed from a 300 V battery. A pulse of 120° duration is used to trigger the appropriate device in each half cycle. The rms value of the fundamental component of the output voltage, in volts, is

Solution:

*Answer can only contain numeric values

QUESTION: 61

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.

Solution:

*Answer can only contain numeric values

QUESTION: 62

In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady state current through the 1Ω resistor, in amperes, is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 63

A dc voltage with ripple is given by v(t) = [100+10sin(ωt) - 5sin(3ωt)] volts. Measurements of this voltage v(t), made by moving-coil and moving iron voltmeters, show readings of V_{1} and V_{2} resplectively. The value of V_{2}-V_{1}, in volts, is ___________.

Solution:

*Answer can only contain numeric values

QUESTION: 64

The circuit below is excited by a sinusoidal source. The value of R, in Ω for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

Solution:

*Answer can only contain numeric values

QUESTION: 65

In the circuit shown below, the node voltage V_{A} is _____________V.

Solution:

### Syllabus - Electrical Engineering, GATE

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