GATE 2020 Electrical Engineering Previous Year Paper

GATE 2020 Electrical Engineering Previous Year Paper

Q.1 NPA is the asset that a customer borrows and holds it for a period of time without paying any interest. RBI has reduced the holding period for NPA thrice during the period 1993- 2004. In 1993 it was four quarters (360 days) how many days is the holding period in 2004? 

(a) 90 

(b) 180 

(c) 45 

(d) 270 

Ans. (a) 

 

Q.2 Number between 1001 to 9999 how many times 37 occurs in the same sequence? 

(a) 279 

(b) 280 

(c) 270

(d) 299 

Ans. (a) 

 

Q.3 The revenue and expenditure of four companies P, Q, R, S as shown in the figure below company Q earns a profit of 10% on expenditure of 2014, the revenue of Q in 2015 is ________. 

Ans. Data insufficient 

 

Q.4 Stock markets _______ at the news of the coup. 

(a) plugged 

(b) plunged 

(c) probed 

(d) poised 

Ans. (b) 

 

Q.5 This book, including all its chapters, ________ interesting. The students as well as instructor ________ in agreement with it. 

(a) is, was 

(b) is, are 

(c) were, was 

(d) are, are 

Ans. (b) 

 

Q.6 People were prohibited ________ there vehicles near the entrance of the main administrative building. 

(a) to park 

(b) to have parked 

(c) from parking 

(d) parking 

Ans. (c) 

 

Q.7 Select the word do :

undo : : trust : 

(a) distrust 

(b) entrust 

(c) intrust 

(d) untrust 

Ans. (a) 

 

Q.8 Find the ratio of AC+BC / AB 

AB where O is center of the circle shown below. 

AB , AC and BC are chords. 

Ans. (1.414) 

 

Q.9 Z : WV : RQP : ? 

(a) KIJH 

(b) JIHG 

(c) HIJK 

(d) KJIH 

Ans. (d) 

 

Q.10 If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed with Q as a member? 

(a) 5 

(b) 7 

(c) 8 

(d) 6 

Ans. (b) 

 

Q.11 A resistor and a capacitor are connected in series to a 10 V dc supply through a switch is closed at t = 0, and the capacitor voltage is found to cross ‘0’ voltage at t = 0.4τ (τ = time constant). The absolute value of % change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is _____. 

Ans. (54.989) 

 

Q.12 To ensure the maximum power transfer across V_th the values of R₁ and R₂ will be (Diode in figure is silicon diode) 

(a) R₁ high, R₂ high 

(b) R₁ low, R₂ low 

(c) R₁ low, R₂ high 

(d) R₁ high, R₂ low 

Ans. (b) 

 

Q.13 For the given circuit the value of V_th is ______. 

Ans. (14) 

 

Q.14 In the given circuit rms value of I₁ is _____.

Ans. (1.732) 

 

Q.15 If 

2001 → 98H 

2002 → B1H 

LXI H, 2001H 

MVI A, 21H 

INX H 

ADD M 

INX H 

MOV M, A 

HLT 

The content of 2003H is (_____)₁₀. 

Ans. (210)

 

Q.16 A differential equation with y(t) → output and x(t) → input is 

The poles of the input 

(a) –2j, +2j 

(b) +4, –4 

(c) –2, +2 

(d) +4j, –4j 

Ans. (a) 

 

Q.17 A PMDC motor is connected to 5 V at t = 0. Its speed increases from 0 to 6.32 rad/ sec monotonically from t = 0 to t = 0.5s and finally settles down to 10 rad/sec. Assume negligible armature inductance. Find the transfer function? 

Ans. (c) 

 

Q.18 For the given open loop transfer function . If 1 + G(s)H(s) plane  encircles the origin once in counter clockwise direction then number of closed loop poles in right side of s-plane will be 

Ans. (0) 

 

Q.19 For the given open loop transfer function with unity negative feedback gain, 

K The value of gain K. For which closed loop system is marginally stable will be _________ . 

Ans. (8)

 

Q.20 A stable LTI system with single pole P, has a transfer function G(s)H(s) = s2 + 100s – P with DC gain of 5; the smallest possible frequency in radian/sec at only gain is 

(a) 11.08 

(b) 70.13 

(c) 122.07 

(d) 8.84 

Ans. (d) 

 

Q.21 For the given block diagram of the system 

Which of the following is true regarding order and stability of the system 

(a) 4^th order and stable 

(b) 4^th order and unstable 

(c) 3^rd order and unstable 

(d) 3^rd order and stable 

Ans. (b) 

 

Q.22 Which of the given below signal flow is analogous to given below system? 

Ans. () 

 

Q.23 Given , find electric flux crossing the cylinder ρ = 3 m; 3 varying from 0 to 5. 

Ans. (180π) 

 

Q.24 The vector function expressed by 

F = a_x(5y – k₁ z) + a_y(3z + k₂ x) + a_z(k₃ y – 4x) 

represent a conservative field, where a_x, a_y, a_z are unit vector along x, y, z directions, respectively the value of constant k₁, k₂ and k₃ ________. 

(a) 4, 5, 3 

(b) 8, 3, 7 

(c) 0, 0, 0 

(d) 3, 8, 5 

Ans. (a) 

 

Q.25 The value of mutual inductance figure shows long wire carrying current 2 A placed in away from square coil as shown in figure. The value mutual inductance will be ____. nH. 

Ans. (138.6) 

 

Q.26 In a dielectric medium in cylindrical, then find volume charge density 

(a) 2∈_o 

(b) 3∈_o 

(c) 4∈_o 

(d) 9∈_o 

Ans. (d) 

 

Q.27 In the given figure, the three windings having polarity as shown above, are connected to 3-φ, balanced supply. The number of turns in the supply winding is 20, the voltage seen in winding X having N = 2 turns will be 

Ans. (46)

 

Q.28 A cylindrical rotor synchronous generator delivering constant active power at a constant terminal voltage, a current of 100 A at a 0.9 p.f. lagging. A shunt reactor is connected so that the reactive power demand doubles then the new value of armature current is ______ A. 

Ans. (125.29) 

 

Q.29 A cylindrical rotor generator having internal emf 1 + j0.7 V and terminal voltages (1 + j 00 V). The synchronous reactance is 0.7 pu whereas subtransient reactance is 0.2 pu for 3-φ bolted short circuit at generator the value of subtransient generated internal emf is ______. 

Ans. (1.019) 

 

Q.30 4 kVA, 200/100 V, 50 Hz single phase transformer has no load core loss of 450 W. If high voltage side is energized by 160 V, 40 Hz, the core loss will be 320 W. Find the core loss if the high voltage side is energized by 100 V, 25 Hz. 

Ans. (162.5) 

 

Q.31 A 3-φ, 50 Hz, 4 pole induction motor runs at no load with a slip of 1%, at full load the motor runs at a slip of 5%. The percentage speed regulation of the motor is _____. 

Ans. (4.02) 

 

Q.32 A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequence detectable. For the sequence (1, 0, 1) and input data (1,1,0,1,0,0,1,1,0,1,0,1,1,0) the output is 

Ans. () 

 

Q.33 A synchronous generator has lossless reactance X_s. Then V_A is terminal voltage and E_f is internal emf voltage. 

P : If power factor is leading then always V_A > E_f 

Q : If power factor is lagging then always V_A < E_f 

Which of the statement is true? 

(a) P is false, Q is true 

(b) P is false, Q is false 

(c) P is true, Q is true 

(d) P is true, Q is false 

Ans. (a) 

 

Q.34 A 250 DC shunt motor having armature resistance of 0.2 Ω and field resistance of 100 Ω. It draws a no load current of 5 A at 1200 rpm. The brush drop is 1 V per brush at all operating conditions. If the motor draws 50 A at full load and flux per pole is decreased by 5% because of armature reaction. The speed of the motor at full load is ____ rpm. 

(a) 900 

(b) 1000 

(c) 1200 

(d) 1220 

Ans. (d) 

Q.35 Find Z(unsaturated)Z(Saturated)=?

Ans. (2.05) 

 

Q.36 DC bias voltage of 13 V is applied between gate and body time. The charge measured in the silicon dioxide layer is +Q, 

The total charge in the box region is ________ multiple of +Q. (Give answer to nearest integer) 

Ans. (#)A 

 

Q.37 A diode is biased of –0.03 V having an ideality factor of 15/13; and V_T = 26 mV; if the current has to be rased to 1.5 times of the than required voltage will be 

(a) –4.5 V 

(b) –0.09 V 

(c) –0.02 V 

(d) None of above 

Ans. (c)

 

Q.38 For a common source amplifier g_m = 520 μA/V² and r_d = 4.7 kΩ calculate gain of amplifier. 

(a) –2.447 

(b) 

(c) 

(d) 

Ans. (a) 

 

Q.39 A causal control system having poles at (–2, 1), (2, –1) and zeros at (2, 1) and (–2, –1). Identify the nature of transfer function. 

(a) Unstable, complex, all pass 

(b) Stable, real, all pass 

(c) Unstable, complex, HP 

(d) Stable, real, HPF 

Ans. (a)

All pass filters because poles and zeros are mirror-image of each other (i..e for each pole there is a mirror-image zero). Unstable because one pole in the RHS of s-plane. 

Transfer function is complex. 

h(t) or impulse response will be also complex because poles are not occuring in conjugate pairs as well as zeros are also not occuring in conjugate pair.

 

Q.40 x(t) ∗ h(t) = y(t), where h(t) is an impulse response. 

|x(t)| ∗ |h(t)| = z(t) then which of the following is correct. 

(a) For every –∞ < t < ∞, z(t) ≤ y(t) 

(b) For every –∞ < t ≤ ∞, z(t) ≥ y(t) 

(c) For some –∞ < t < ∞, z(t) ≤ y(t) 

(d) For some –∞ < t ≤ ∞, z(t) ≥ y(t) 

Ans. (b) 

Since, y(t) = x(t) + h(t) 

and z(t) = x () t × ht () 

Case-1: x( )t 

then, y(t) and z(t) 

Case-2: x( )t 

then, y(t) = z(t) 

Thus, z(t) ≥ y(t), for all ‘t’ 

 

Q.41 A signal x(n) is given by (½)ⁿ 1(n) where, 

Z-transform x(n – K) is ^, then what will be ROC of x(n – K) 

(a) Z > ½ 

(b) Z < 2 

(c) Z > 2 

(d) Z < ½ 

Ans. (a) 

 

Q.42 If x_A and x_R are average and rms values of signal x(t) = x(t – T) respectively. y_A and y_R are average and rms value of signal y(t) = Kx(t) respectively. K and T are independent of t. 

(a) y_A = Kx_A, y_R = Kx_R 

(b) y_A ≠ Kx_A, y_R = Kx_R 

(c) y_A = Kx_A, y_R ≠ Kx_R 

(d) y_A ≠ Kx_A, y_R ≠ Kx_R 

Ans. (a) 

Given that, 

⇒ Average x(t) = X_a , Rms x(t) = X_R

⇒ Average y(t) = Y_a , Rms y(t) = Y_R 

⇒ x(t) = x(t – T) 

⇒ y(t) = Kx(t) …(i) 

⇒ Y_a = KX_a 

Since, Power y(t) = |K|² power x(t) 

⇒ Rms y²(t) = |K|² Rms x ² ( t ) 

⇒ Rms y(t) = |K|² Rms x ( t ) 

⇒ Y_R = |K|X _R 

Assuming K as real and positive, 

Y_R = KX_R 

 

Q.43 Which of the following statement is true about the two sided Laplace transform? 

(a) It always exists for a signal that may or may not have Fourier transform. 

(b) It has no poles for any bounded signal that is non-zero only inside a finite time interval.

(c) If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace transform will have no poles. 

(d) The number of finite poles finite zeros must be equal. 

Ans. (b) 

 

Q.44 A 50 Hz, power system network is operated under load of 100 MW. When the load is increased, the power input by the synchronous generator is increased by 10 MW and frequency of the rpm falls to 49.75 Hz. What will be the load at power system for the frequency falls to 49.25 Hz? 

Ans. (130) 

Assumed full load frequency is 50 Hz

 

Q.45 Find admittance matrix 2 bus is connected by 2 transformers having ratios 1 : T_i and T_j : 1 respectively and line having Y admittance. 

 

Q.46 A transmission line is being protected by distance protection. 80% of the line is being protected. The transfer reactance is 0.2 p.u. A solid 3-φ, fault occurred at the end of the transmission line. The minimum level of fault current to activate the relay 

(a) 6.25 

(b) 5 

(c) 1.25 

(d) 3 

Ans. (a) 

 

Q.47 Voltage at bus 1 = 1.1 p.u. Voltage at bus 2 = 1 p.u. 

Voltage at bus 2 is kept constant, Q₁₂ is the sending reactive power from 1 to 2. On changing the bus 1 voltage, Q₁₂ increases by 20%. Active power is zero in both the condition find the new value of bus 1 voltage. 

Ans. (#)A 

 

Q.48 In AC voltage controller shown below. Thyristor T₁ is fired at α and T₂ is fired at 180° + α. To control the output power over range 0 to 2 kW. The minimum range of variation in α is 

(a) 0° to 60° 

(b) 0° to 120° 

(c) 60° to 120° 

(d) 60° to 180°# 

Ans. (d) 

 

Q.49 A 1-φ, fully controlled rectifier is connected to highly inductive RL load with R = 10 Ω at 230 V, 50 Hz. The source inductance is 2.28 mH. If the firing angle α = 45°, then the overlapping angle will be 

Ans. (4.25) 

 

Q.50 Value of σ adjusted so that 3^rd harmonic is completely eliminated. Find the percentage magnitude of 5^th harmonic w.r.t. fundamental component at this condition. 

Ans. (20) 

 

Q.51 A single-phase, 50 Hz full bridge rectifier with highly inductive RL load. The two most dominant frequency components will be 

(a) 50 Hz, 150 Hz 

(b) 50 Hz, 100 Hz 

(c) 150 Hz, 250 Hz 

(d) 50 Hz, 0 Hz 

Ans. (a) 

1-φ full bridge rectifier, 

n = 1, 3, 5, … 

f = 50, 150, 250 dominant 

 

Q.52 A DC-DC converter shown below having switching frequency of 10 kHz with duty ratio 0.6. All the components are ideal and the initial inductor current is zero. Energy stored in the inductor (in mJ) at the end of 10 switching cycles is 

Ans. (5)

Buck boost converter

 

Q.53 R_T → Thermistor R_T = 2(1 + αT) Temperature rise = 150% Find errors in the output voltage? 

R₁ = 1 kHz, R₂ = 1.3 kΩ, R₃ = 2.6 kΩ 

Ans. () 

 

Q.54 A vector function is given by . The line integral of the above function along the curve C given by y = x² as shown below ________. 

Ans. (–2.33) 

 

Q.55 dy/dx = 2x – y, y(0) = 1. Find y at x = ln2 

Ans. (0.886) 

 

Q.56 Value of integral z2 + 1z2 – 2z along the contour |z| = 1 is 

(a) πi 

(b) –πi 

(c) 8πi 

(d) –8πi 

Ans. (b) 

 

Q.57 The number of purely real elements in lower triangular representation of given 3 × 3 matrix obtained through given decomposition is 

Ans. (#) 

 

 

Q.58 If y = 3x² + 3x + 1, for x∈[–2, 0], find maximum and minimum value in the given range. 

(a) 4 and 1 

(b) 7 and ¼ 

(c) ¼ and 1 

(d) –2 and 1/-2 

Ans. (b) 

 

Q.59 Which of the following is true? 

Ans. (d)