Category: GATE

GATE 2016 Electrical Engineering Session 2

Q. 1 The chairman requested the aggrieved shareholders to _________________ him.

A. bare with

B. bore with

C. bear with

D. bare

 

Q. 2 Identify the correct spelling out of the given options:

A. Managable

B. Manageable

C. Mangaeble

D. Managible

 

Q. 3 Pick the odd one out in the following:13, 23, 33, 43, 53

A. 23

B. 33

C. 43

D. 53

 

Q. 4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.Which of the following can be logically inferred from the above statements?

A. R2D2 is a robot which can only repair aeroplanes

B. R2D2 is the only robot which can repair aeroplanes

C. R2D2 is a robot which can repair only aeroplanes

D. Only R2D2 is a robot

 

Q. 5 If |9y−6| =3, then y² −4y/3 is ______.

A. 0

B. +1/3

C. -1/3

D. undefined

 

Q. 6 The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is____.

 

Q. 7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed that mechanical engineering is a profession unsuitable for women. A research study on women with masters or higher degrees in mechanical engineering found that 99 % of such women were successful in their professions.Which of the following can be logically inferred from the above paragraph?

A. Many students have misconceptions regarding various engineering disciplines

B. Men with advanced degrees in mechanical engineering believe women are well suited to be mechanical engineers

C. Mechanical engineering is a profession well suited for women with masters or higher degrees in mechanical engineering.

D. The number of women pursuing higher degrees in mechanical engineering is small.

 

Q. 8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a developing country.

Which of the following can be logically inferred from the above sentence?Based on the

Proposal, (i)In the initial years, SIT students will get degrees from IIT.

(ii)SITs will have a distinct national objective.

(iii)SITs will have a distinct national objective.

(iv)SITs will serve technological needs of a developing country

A. (iii) and (iv) only

B. (i) and (iv) only

C. (ii) and (iv) only.

D. (ii) and (iii) only

 

Q. 9 Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will

successfully make exactly 6 free throws in 10 attempts? 

A. 0.2508

B. 0.2816

C. 0.2934

D. 0.6000

 

Q. 10 The answer of the numerical is

 

Q. 11 The output expression for the Karnaugh map shown below is

A. A+B̅

B. A+C̅

C. A̅+C̅

D. A̅+C

 

Q. 12 The circuit shown below is an example of a

A. low pass filter

B. band pass filter

C. High pass filter

D. notch filteR

 

Q. 13 The following figure shows the connection of an ideal transformer with primary to

secondary turns ratio of 1:100. The applied primary voltage is 100 V (rms), 50 Hz, AC. The rms value of the current I, in ampere, is __________

 

Q. 14 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 15 Suppose the maximum frequency in a band-limited signal x(t) s 5 kHz. Then, the maximum frequency in x(t)cos(2000πt),in kHz, is ________

 

Q. 16 Consider the function ݂f(z)= z + z* where z*is a complex variable and ∗ݖdenotes its complex conjugate. Which one of the following is TRUE?

A. f(z) is both continuous and analytic

B. f(z) is continuous but not analytic

C. f(z) is not continuous but is analytic

D. f(z) is neither continuous nor analytic

 

Q. 17 A 3 × 3 matrix ܼܿP is such that P³=P ܼܿ. Then the eigenvalues of ܼܿ are

A. 1, 1, −1

B. 1, 0.5 + ݆j0.866, 0.5 − ݆j0.866

C. 1, −0.5 + ݆j0.866, −0.5 − ݆j0.866

D. 0, 1, −1

 

Q. 18 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 19 Choose the correct option

A. 0

B. 2

C. 4

D. 6

 

Q. 20 Let f(x) be a real, periodic function satisfying ݂f(-x)=-f(x) The general form of its Fourier series representation would be.

A. A

B. B

C. C

D. D

 

Q. 21 A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz ac source as shown in the figure below. The rms values of plausible voltages across the resistance (VR) and coil (VC) respectively, in volts, are

A. 65, 35

B. 50, 50

C. 60, 90

D. 60, 80

 

Q. 22 The voltage (V) and current (A) across a load are as follows.

v(t) = 100sin(ωt),

i(t) = 10sin(ωt – 60∘) + 2sin(ωt) + 5sin(5ωt)

The average power consumed by the load, in W, is ________.

 

Q. 23 A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six overcurrent relays R1 to R6. Assuming a mix of directional and nondirectional relays at appropriate locations, the remote backup relays for R4 are

A. R1, R2

B. R2, R6

C. R2, R5

D. R1, R6

 

Q. 24 A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is

A. 189 x 189

B. 100 x 100

C. 90 x 90

D. 180 x 180

 

Q. 25 The inductance and capacitance of a 400 kV, three-phase, 50 Hz lossless transmission line are 1.6 mH/km/phase and 10 nF/km/phase respectively. The sending end voltage is maintained at 400 kV. To maintain a voltage of 400 kV at the receiving end, when the line is delivering 300 MW load, the shunt compensation required is

A. capacitive

B. inductive

C. resistive

D. zero

Q. 26 A parallel plate capacitor filled with two dielectrics is shown in the figure below. If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is 

A. 1

B. 2

C. 4

D. 16

 

Q. 27 A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a

synchronous reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is ______.

 

Q. 28 Consider a linear time-invariant system with transfer function

If the input cos(t) is and the steady state output is A cos(t+α) then the value of A is _________.on

 

Q. 29 A three-phase diode bridge rectifier is feeding a constant DC current of 100 A to a highly inductive load. If three-phase, 415 V, 50 Hz AC source is supplying to this bridge rectifier then the rms value of the current in each diode, in ampere, is _________.

 

Q. 30 A buck-boost DC-DC converter, shown in the figure below, is used to convert 24 V battery voltage to 36 V DC voltage to feed a load of 72 W. It is operated at 20 kHz with an inductor of 2 mH and output capacitor of 1000 μF. All devices are considered to be ideal. The peak voltage across the solid-state switch (S), in volt, is

 

Q. 31 For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase lag occurs is, ___________

 

Q. 32 The direction of rotation of a single-phase capacitor run induction motor is reversed by

A. interchanging the terminals of the AC supply

B. interchanging the terminals of the capacitor

C. interchanging the terminals of the auxiliary winding

D. interchanging the terminals of both the windings

 

Q. 33 In the circuit shown below, the voltage and current sources are ideal. The voltage (Vout) across the current source, in volts, is

A. 0

B. 5

C. 10

D. 20

 

Q. 34 The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are

A. 2 and 5

B. 5 and 2

C. 3 and 4

D. 4 and 3

 

Q. 35 Two electrodes, whose cross-sectional view is shown in the figure below, are at the same potential.

The maximum electric field will be at the point

A. A

B. B

C. C

D. D

 

Q. 36 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 37 For the circuit shown below, taking the opamp as ideal, the output voltage Vout in terms of the input voltages V1 , V2 and V3 is

A. 1.8V1 + 7.2V2 -V3

B. 2V1 + 8V2 – 9V3

C. 7.2V1 + 1.8V2 -V3

D. 8V1 + 2V2 – 9V3

 

Q. 38 Choose the correct option

A. 2B1

B. 2(B1+B2)

C. 4(B1+B2)

D. ∞

 

Q. 39 Choose the correct option

A. 0

B. 0.5

C. 1

D. 2

 

Q. 40 Answer is ___________

 

Q. 41 The line integral of the vector field F = 5xz î + (3x² + 2y) ĵ + x²z k ̂ along a path from (0,0,0) to (1,1,1) parametrized by (t,t²,t) is _____

 

Q. 42 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 43 Choose the correct option

A. 2, ଵ 2, ଵ 2,1/2

B. 4,1/2

C. 2,1/4

D. 4,1/4

 

Q. 44 The driving point input impedance seen from the source Vs of the circuit shown below, in Ω, is ______.

 

Q. 45 The z-parameters of the two port network shown in the figure are z11 = 40 Ω, z12 = 60 Ω, z21 = 80 Ω and z22 =100 Ω. . The average power delivered to Rl=20 Ω, in watts, is _______

 

 

Q. 46 In the balanced 3-phase, 50 Hz, circuit shown below, the value of inductance (L) is 10 mH. The value of the capacitance (C) for which all the line currents are zero, in millifarads, is ___________.

 

 

Q. 47 In the circuit shown below, the initial capacitor voltage is 4 V. Switch S1 is closed at t=0. The charge (in μC) lost by the capacitor from t= 25μs ro t= 100μs is _________.

 

Q. 48 The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in the system are also shown in the figure. The infinite bus voltage magnitude is 1.0 p.u. A three phase fault occurs at the middle of line 2. The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is _________.

 

Q. 49 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 50 At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ________.

 

Q. 51 The power consumption of an industry is 500 kVA, at 0.8 p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is 100 kW, the p.f. of the motor is _____________

 

Q. 52 The flux linkage (λ) and current (i) relation for an electromagnetic system is λ = (√i)/g .When i = 2A and ݃g (air-gap length) = 10 cm, the magnitude of mechanical force on the moving part, in N, is ________.

 

Q. 53 The starting line current of a 415 V, 3-phase, delta connected induction motor is 120 A, when the rated voltage is applied to its stator winding. The starting line current at a reduced voltage of 110 V, in ampere, is _________

 

Q. 54 A single-phase, 2 kVA, 100/200 V transformer is reconnected as an auto-transformer such that its kVA rating is maximum. The new rating, in kVA, is ______.

 

Q. 55 A full-bridge converter supplying an RLE load is shown in figure. The firing angle of the bridge converter is 120º. The supply voltage Vm (t) = 200Π sin(100 Πt) V, R=20 Ω, E=800 V. The inductor L is large enough to make the output current IL a smooth dc current. Switches are lossless. The real power fed back to the source, in kW, is _______.

 

Q. 56 A three-phase Voltage Source Inverter (VSI) as shown in the figure is feeding a delta connected resistive load of 30 Ω/phase. If it is fed from a 600 V battery, with 180o conduction of solid-state devices, the power consumed by the load, in kW, is ________.

 

Q. 57 A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400 V, at a power of 4 kW. All devices are ideal. Considering continuous inductor current, the rms current in the solid state switch (S), in ampere, is _________.

 

Q. 58 A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All devices are ideal. It is used to charge a battery at 400 V with power of 5 kW from a source Vs = 220 V (rms), 50 Hz sinusoidal AC mains at unity p.f. If its AC side interfacing inductor is 5 mH and the switches are operated at 20 kHz, then the phase shift (δ) between AC mains voltage (Vs) an fundamental AC rms VSC voltage (VC1), in degree, is ________.

 

Q. 59 Choose the correct option

A. A

B. B

C. C

D. D

 

Q. 60 Choose the correct Option

A. A

B. B

C. C

D. D

 

Q. 61 Three single-phase transformers are connected to form a delta-star three-phase

transformer of 110 kV/ 11 kV. The transformer supplies at 11 kV a load of 8 MW at 0.8 p.f. lagging to a nearby plant. Neglect the transformer losses. The ratio of phase currents in delta side to star side is

A. 1 : 10√3

B. 10√3 : 1

C. 1 : 10

D. √3 : 10

 

Q. 62 Choose the correct option

A. 1

B. 2

C. 5

D. 9

 

Q. 63 Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and j0.15 p.u., respectively. If the pre-fault voltage is 1 p.u., for a line-to-ground (L-G) fault at the terminals of the generators, the fault current, in p.u., is ______.

 

 

Q. 64 An energy meter, having meter constant of 1200 revolutions/kWh, makes 20 revolutions in 30 seconds for a constant load. The load, in kW, is _________.

 

Q. 65 A rotating conductor of 1 m length is placed in a radially outward (about the z-axis) magnetic flux density (B) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1 m distance from the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1 V across it, should be ____________.

 

 

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	B	B	B	C	120	C	C	A	7
Question	11	12	13	14	15	16	17	18	19	20
Answer	B	A	9.5 to 10.5	D	6	B	D	A	B	B
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	249 to 251	D	A	B	C	4.9 to 5.1	0.69 to 0.72	57 to 58	59.5 to 60.5
Question	31	32	33	34	35	36	37	38	39	40
Answer	0.3 to 0.33	C	D	D	A	D	D	B	D	7 to 7.5
Question	41	42	43	44	45	46	47	48	49	50
Answer	4.4 to 4.45	D	A	19.5 to 20.5	34 to 36	2.9 to 3.1	6.8 to 7.2	2.2 to 2.35	C	294 to 298
Question	51	52	53	54	55	56	57	58	59	60
Answer	0.31 to 0.33	186 to 190	31 to 33	5.9 to 6.1	5.9 to 6.1	23 to 25	3 to 4	9.1 to 9.3	A	B
Question	61	62	63	64	65
Answer	A	A	5.5 to 6.5	1.9 to 2.1	9.4 to 9.7

GATE 2016 Electrical Engineering Session 1

Q. 1 The man who is now Municipal Commissioner worked as ___________________ .

A. the security guard at a university

B. a security guard at the university

C. a security guard at university

D. the security guard at the university

 

Q. 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.

A. put up with

B. put in with

C. put down to

D. put up against

 

Q. 3 Find the odd one in the following group of words:

Mock, Deride, Praise, Jeer

A. Mock

B. Deride

C. Praise

D. Jeer

 

Q. 4 Find the odd one from the following options.

A. CADBE

B. JHKIL

C. XVYWZ

D. ONPMQ

 

Q. 5 In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of (α^n + β^n) / (α^-n + β^-n)

A. n^4

B. 4^n

C. 2^2n – 1

D. 4^n – 1

 

Q. 6 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 __________.

A. 35

B. 45

C. 65

D. 90

 

Q. 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

A. (i) only

B. (ii) only

C. both (i) and (ii)

D. neither (i) nor (ii)

 

Q. 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 is not a hill-station.

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

A. (i) only

B. (ii) only

C. both (i) and (ii)

D. neither (i) nor (ii)

 

Q. 9 In a 2 x 4 rectangle grid shown in figure (1), each cell is a rectangle. How many rectangles can be observed in the grid?

A. 21

B. 27

C. 30

D. 36

 

Q. 10 Choose the correct expression for f(x) given in the graph in figure (1).

A. f(x) = 1 – |x – 1|

B. f(x) = 1 + |x – 1|

C. f(x) = 2 – |x – 1|

D. f(x) = 2 + |x – 1|

 

Q. 11 The maximum value attained by the function f(x) = x (x – 1) (x – 2) in the interval [1, 2] is __________ .

 

Q. 12 Consider a 3 x 3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________.

 

Q. 13 The Laplace Transform of f(x) = e^2t sin (5t) u(t) is

A. 5 / s^2 – 4s + 29

B. 5 / s^2 + 5

C. s – 2 / s^2 – 4s + 29

D. 5 / s + 5

 

Q. 14 A function y(t), such that y(0) = 1 and y(1) = 3e^-1, is a solution of the differential equation d^2y / dt^2 + 2 (dy / dt) + y = 0. Then y(2) is

A. 5e^-1

B. 5e^-2

C. 7e^-1

D. 7e^-2

 

Q. 15 Find the value of integral given in figure (1), over the contour |z| = 1, taken in the anticlockwise direction, would be:

A. 24πi / 13

B. 48πi / 13

C. 24 / 13

D. 12 / 13

 

Q. 16 The transfer function of a system is Y(s) / R(s) = s / s + 2. The steady state output y(t) is A cos (2t + φ) for the input cos(2t). The values of A and φ, respectively are

A. 1 / √2, – 45°

B. 1 / √2, +45°

C. √2, -45°

D. √2, +45°

 

Q. 17 The phase crossover frequency of the transfer function G(s) = 100 / (s + 1)^3 in rad/s is 

A. √3

B. 1 / √3

C. 3

D. 3√3

 

Q. 18 Consider a continuous-time system with input x(t) and output y(t) given by

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

A. linear and time-invariant

B. nonlinear and time-invariant

C. linear and time-varying

D. nonlinear and time-varying

 

Q. 19 Find the value of the given function given in figure (1), where δ(t) is the Dirac delta function, is

A. 1 / 2e

B. 2 / e

C. 1 / e^2

D. 1 / 2e^2

 

Q. 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

A. 8

B. 10

C. 12

D. 14

 

Q. 21 Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure (1). The Boolean expression for output F in terms of A and B is

A. A

B. B

C. C

D. D

 

Q. 22 A transistor circuit is given below. The Zener diode breakdown voltage is 5.3 V as shown in figure (1). Take base to emitter voltage drop to be 0.6 V. The value of the current gain β is _________.

 

Q. 23 In cylindrical coordinate system, the potential produced by a uniform ring charge is given by φ = f (r, z), where f is a continuous function of r and z. Let ⃗E be the resulting electric field. Then the magnitude of ∇ × ⃗E

A. increases with r

B. Is 0

C. Is 3

D. Decreases with z

 

Q. 24 A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability μ, of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ____.

 

Q. 25 RA and RB are the input resistances of circuits as shown in figure (1). The circuits extend infinitely in the direction shown. Which one of the following statements is TRUE?

A. RA=RB

B. RA=RB=0

C. RA< RB

D. RB= RA /(1+RA)

 

Q. 26 In a constant V / f induction motor drive, the slip at the maximum torque

A. is directly proportional to the synchronous speed.

B. remains constant with respect to the synchronous speed.

C. has an inverse relation with the synchronous speed.

D. has no relation with the synchronous speed

 

Q. 27 In the portion of a circuit shown in figure (1), if the heat generated in 5 Ω resistance is 10 calories per second, then heat generated by the 4 Ω resistance, in calories per second, is _______.

 

Q. 28 In the given circuit shown in figure (1), the current supplied by the battery, in ampere, is _________________ .

 

Q. 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 he PV buses are converted to PQ type. In this iteration,

A. the number of unknown voltage angles increases by two and the number of unknown voltage magnitudes increases by two

B. the number of unknown voltage angles remains unchanged and the number of unknown voltage magnitudes increases by two.

C. the number of unknown voltage angles increases by two and the number of unknown voltage magnitudes decreases by two

D. the number of unknown voltage angles remains unchanged and the number of unknown vp;tage magnitudes decreases by two

 

Q. 30 The magnitude of three-phase fault currents at buses A and B of a 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 _________________.

 

Q. 31 Consider a system consisting of a synchronous generator working at a lagging power factor, a synchronous motor working at an over excited condition and a directly grid connected induction generator. Consider capacitive V Ar to be a source and inductive V Ar to be a sink or reactive power. Which one of the following statements is TRUE?

A. Synchronous motor and synchronous generator are sources and induction generator is a sink of reactive power. 

B. Synchronous motor and induction generator are sources and synchronous generator is a sink of reactive power.

C. Synchronous motor is a source and induction generator and synchronous generator are sinks of reactive power.

D. All are sources of reactive power.

 

Q. 32 A buck converter, as shown in Figure (a), 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 ________.

 

Q. 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 Figures (b) and (c), respectively. The conduction power loss in the power module (S, D), in watts, is ________.

 

Q. 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 the figure (A), (B), (C), (D)

 

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 35 If an ideal transformer has an inductive load element at port 2 as shown in the figure (1), the equivalent inductance at port 1 is

A. nL

B. n^2L

C. n / L

D. n^2 / L

 

Q. 36 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 _________.

 

Q. 37 The value of S is given in the figure (1) where |α| < 1. The value of α in the range 0 < α < 1, such that S = 2α is _______________.

 

Q. 38 Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 − 3A + 4I would, respectively, be 

A. 2, 14; x1, x2

B. 2, 14; x1 + x2, x1 – x2

C. 2, 0; x1, x2

D. 2, 0; x1 + x2, x1 – x2

 

Q. 39 Let A be a 4 x 3 real matrix with rank 2. Which one of the following statement is TRUE?

A. Rank of A^T A is less than 2

B. Rank of A^T A is equal to 2

C. Rank of A^T A is greater than 2

D. Rank of A^T A can be any number between 1 and 3

 

Q. 40 Consider the following asymptotic Bode magnitude plot given in figure (1) (ω is in rad/s). Which one of the following transfer functions is best represented by the above Bode magnitude plot?

A. 2s / (1 + 0.5s) (1 + 0. 25s)^2

B. 4 (1 + 0.5s) / s (1 + 0.25s)

C. 2s / (1+ 2s) (1 + 4s)

D. 4s / (1+ 2s) (1 + 4s)^2

 

Q. 41 Consider the following state-space representation of a linear time-invariant system given in figure (1).

The value of y(t) for (t) = log e 2 is _____________.

 

Q. 42 Loop transfer function of a feedback system is G(s) H(s) = s + 3 /s^2 (s – 3). Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s) H(s) encircles – 1 + j0. 

A. once in clockwise direction

B. twice in clockwise direction

C. once in anticlockwise direction

D. twice in anticlockwise direction

 

Q. 43 Given the following polynomial equation:

s^3 + 5.5 s^2 + 8.5 s + 3 = 0,

the number of roots of the polynomial, which have real parts strictly less than -1, is ___________.

 

Q. 44 Suppose x1(t) and x2(t) have the Fourier transforms as shown in figure (1).

Which one of the following statements is TRUE?

A. x1(t) and x2(t) are complex and x1(t) x2(t) is also complex with nonzero imaginary part

B. x1(t) and x2(t) are real and x1(t) x2(t) is also real

C. x1(t) and x2(t) are complex but x1(t) x2(t) is real

D. x1(t) and x2(t) are imaginary but x1(t) x2(t) is real

 

Q. 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)} = γ z(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?

A. cos(t) is an eigen-signal but sin(t) is not

B. cos(t) and sin(t) are both eigen-signals but with different eigenvalues

C. sin(t) is an eigen-signal but cos(t) is not

D. cos(t) and sin(t) are both eigen-signals with identical eigenvalues

 

Q. 46 The current state QA QB 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 given in figure (1) is

A. 00

B. 01

C. 11

D. 10

 

Q. 47 A 2-bit flash Analog to Digital Converter (ADC) is given below. The input is 0 ≤ VIN ≤ 3 Volts. The expression for the LSB of the output B0 as a Boolean function of X2, X1, and X0 is 

A. (a)

B. (b)

C. (c)

D. (d)

 

Q. 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:

A. x = – 2

B. y = 2

C. x^2 + y^2 = 2

D. (x + 2)^2 + y^2 = 16

 

Q. 49 In the circuit shown in figure (1), switch S2 has been closed for a long time. At time t = 0 switch S1 is closed. At t = 0+, the rate of change of current through the inductor, in amperes per second, is __________.

 

Q. 50 A three-phase cable is supplying 800 kW and 600 kV Ar 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 ____________________.

 

Q. 51 A 30 MVA , 3-phase, 50 Hz, 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 Xn (in p.u.) that will limit the positive sequence generator current to 4270 A is __________________. 

 

Q. 52 If the star side of the star-delta transformer shown in figure (1) is excited by a negative sequence voltage, then

A. VAB leads Vab by 60°

B. VAB lags Vab by 60°

C. VAB leads Vab by 30°

D. VAB lags Vab by 30°

 

Q. 53 A single-phase thyristor-bridge rectifier is fed from a 230 V, 50 Hz, single-phase AC mains. If it is delivering a constant DC current of 10 A, at firing angle of 30°, then value of the power factor at AC mains is:

A. 0.87

B. 0.9

C. 0.78

D. 0.45

 

Q. 54 The switches T1 and T2 in Figure (a) are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage vm(t) = 0.8 sin (200πt) V and the triangular carrier voltage (vc) are as shown in Figure (b). The carrier frequency is 5 kHz. The peak value of the 100 Hz component of the load current (iL), in ampere, is ________ .

 

 

Q. 55 The voltage (vs) across and the current (is) through a semiconductor switch during a turn – ON transition are shown in figure (1). The energy dissipated during the turn – ON transition, in mJ, is _____________.

 

Q. 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 ______.

 

Q. 57 A DC shunt generator delivers 45 A at a terminal voltage of 220V. 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 _______________ .

 

Q. 58 A three-phase, 50 Hz salient-pole synchronous motor has a per-phase direct-axis reactance (Xd) of 0.8 pu and a per-phase quadrature-axis reactance (Xq) of 0.6 pu. Resistance of the machine is negligible. It is drawing full-load current at 0.8 pf (leading). When the terminal voltage is 1 pu, per-phase induced voltage, in pu, is _________.

 

Q. 59 A single-phase, 22 kVA, 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 auto-transformer is

A. 22

B. 24.2

C. 242

D. 2420

 

Q. 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 devices in each half cycle. The rms value of the fundamental component of the output voltage, in volts, is

A. 234

B. 245

C. 300

D. 331

 

Q. 61 A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m 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 __________.

 

Q. 62 In the circuit shown in figure (1), the supply voltage is 10 sin (1000t) volts. The peak value of the steady state current through the 1 Ω resistor, in amperes, is _________________ .

 

Q. 63 A dc voltage with ripple is given by v(t) = [100 + 10sin (ωt) – 5 sin (3ωt)] volts. Measurements of this voltage v(t), made by moving-coil and moving-iron voltmeters, show readings of V1 and V2 respectively. The value of V2 – V1, in volts is __________.

 

Q. 64 The circuit given in figure (1) 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 _____________ .

 

 

Q. 65 In the circuit shown in figure (1), the node voltage VA is __________________ V.

 

 

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	A	C	D	B	A	D	D	C	C
Question	11	12	13	14	15	16	17	18	19	20
Answer	0	3	A	B	B	B	A	C	A	B
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	18 to 22	B	99 to 101	D	C	1.9 to 2.1	0.5	B	0.83 to 0.85
Question	31	32	33	34	35	36	37	38	39	40
Answer	A	0.39 to 0.41	169 to 171	C	B	0.2	0.28 to 0.31	A	B	A
Question	41	42	43	44	45	46	47	48	49	50
Answer	5.9 to 6.1	A	2	C	D	C	A	D	1.9 to 2.1	47 to 49
Question	51	52	53	54	55	56	57	58	59	60
Answer	1.05 to 1.15	D	D	9.9 to 10.1	74 to 73	1.4 to 1.5	86 to 88	1.58 to 1.62	C	A
Question	61	62	63	64	65
Answer	1.47	1	0.3 to 0.33	14 to 14.2	11.25 to 11.5