Gate 2022 ELECTRICAL MEMORY BASED QUESTIONS Download App to watch free special classes: Aptitude Q1. Some bottles are cups all cups are knives (a) some bottles are knives (b) some knives are cups (c) All cups are bottles (d) All Knives are cups [Marks 1] Solution Ans: (a) and (b) Q2. As you grow older, an injury to your may take longer to _______. (a) heel/heel (b) heal/heal (c) heal/heel (d) heel/heal [Marks 1] Solution Ans: (d) Q3. There are two identical dice with a single letter on each of the following Q, R, S, T, U &V one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that outcome on the dice were composed only of any combination of the following letters Q, U & V? [Marks 2] Solution Ans: (9/36 or 1/4) Q4. Keep P, Q, R, S, T, U within the hexagonal. Line segment joining RS is greater than segment joining PQ. Line segment RS is perpendicular to PQ and line segment RU is parallel to line segment TQ. Find the correct option. [Marks 2] Solution Ans: (RT is parallel to QS) Q5. 2 shops are S and M. The person who buys from S is Cost price +150 delivery charge. If the buys from M is Cost price +0 delivery charge. Cost price (S) = 0.9* Cost price (M). A person buys the product from S and saves Rs. 100 What’s the cost price at S, excluding delivery charges? [Marks 2] Solution Ans: (2250) Q6. P and Q are in a race, Q starts when P is at 140 m and ratio of speed (Q) = ¾. The gap between P and Q when P wins the race. Track length is 500m. [Marks 1] Solution Ans: (20 m) Q7. 3 Alarms buzz at every 20, 30, 50 mins. Simultaneously buzz at 12 noon, when they will simultaneously buzz again? [Marks 1] Solution Ans: (5 pm) Scan to download app to watch free special classes: Scan to download app to watch free special classes: Gate 2022 Electrical Engineering Solution Discussion Scan to download app to watch free special classes: Technical (EE) Q1. Mathematics 1 0 0 Consider a matrix A = 0 4 −2 the matrix A satisfies the equation 0 1 1 –1 2 6A =A +CA +DI, where C & D are scalars and I is identity matrix. Then (C + D) = _________. [Marks 2] Solution Ans: (5) Q2. Mathematics Let the probability density function of a random variable x be given as f(x) = ae–2|x|. The value of ‘a’ is ________. [Marks 1] Solution Ans: (1) Q3. Mathematics Which not represent area. (a) xdy c ydx (c) dxdy (b) R (d) 1 ( xdy − ydx ) 2 [Marks 1] Solution Ans: (b) Q4 Mathematics Let, f(x,y,z) = 4x2 + 7xy + 3xz2. The direction in which the function f (x, y, z) increases most rapidly at point P = (1, 0, 2) is (a) 20iˆ + 7 ˆj + 12kˆ (b) 20iˆ (c) 20iˆ + 7 ˆj (d) 20iˆ + 12kˆ [Marks 1] Scan to download app to watch free special classes: Solution Ans: (a) Q.5 Mathematics: x Let f ( x ) = et ( t − 1)( t − 2 ) dt . Then f ( x ) decreases in the interval. 0 (a) x ( 0.5,1) (b) x (1, 2 ) (c) x ( 0,1) (d) x ( 2,3 ) [Marks 1] Solution Ans: (b) Q.6 Mathematics: Consider 3 × 3 matrix A where (i, j)th element aij = (i - j)3 the matrix is. (a) Symmetrical (b) Skew symmetric (c) null (d) skull [Marks 1] Solution Ans: (b) Q7. Mathematics: The fig below shows the front and rear views of a disc, which is should with identical patterns. The disc is flipped once with respect to any one if the fixed axes 1 – 1, 2 – 2 or 3 – 3 chosen uniformly at random. What is the probability that the disc does not retain the same front and rear view after the flipping operation? [Marks 2] (a) 1 (b) 0 (c) 2/3 (d) 1/3 Solution Ans: (c) Scan to download app to watch free special classes: Q8. Power electronics A charger supplies 100W at 20V for charging the battery of a laptop. The power device used in the converter inside the charger, operate at a switching frequency of 200KHz. Which power device is belt suited for this purpose? [Marks 1] (a) IGBT (b) MOSFET (c) BJT (d) Thyristor Solution Ans: (b) Q9. Power system The fuel cost functions in rupees 600 MW thermal power plants are given by Plant 1 : C1 = 350 + 6 P1 + 0.004 P12 Plant 2 : C2 = 450 + aP1 + 0.003P22 where 𝑃1 and 𝑃2 are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power ( ) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optional generation of plant 1 plant 2 in MW, respectively are [Marks 2] (a) 200, 350 (b) 350, 200 (c) 325, 225 (d) 250, 300 Solution Ans: (d) Q10. Power Electronics The steady state current flowing through inductor of a DC-DC buck boost converter is below. If peak to peak ripple in output voltage of converter is 1V, then value of output capacitor is _________ (µF) [Marks 2] Solution Ans: (168) Q11. Power Electronics: A single-phase fill bridge diode rectifier feeds a resistive load of 50Ω from a 200V, 50 Hz. single-phase AC supply If the diode are ideal then the active power in watts drawn because the load is _________. (Round of to nearest integer) [Marks 1] Solution Ans: (800) Scan to download app to watch free special classes: Scan to download app to watch free special classes: Q12. Power Electronics: The volt at the input of an AC – DC rectifier is given by V(t) = 230 2 sin ωt where ω = 2π × 50 rad is. The input current drawn by the rectifier is given by i(t)=10 sin (ωt – π/3) + 4 sin (3ωt – π/6) + 3 sin (5ωt – π/3) the input power factor is ________. [Marks 2] Solution Ans: (0.44) Q13. Analog Electronics: Ideal MOSFET is in saturation under CD AMP so small signal current gain (a) 0 (b) (c) 1 (d) 100 Solution Ans: (b) [Marks 1] Q14. Analog Electronics: For the circuit shown below with ideal diodes, the output will be [Marks 1] (a) Vout = Vin for Vin < 0 (c) Vout = -Vin for Vin > 0 Solution Ans: (d) (b) Vout = -Vin for Vin < 0 (d) Vout = Vin for Vin > 0 Q15. Analog Electronics: The current gain (Iout/Iin) in the circuit will an ideal current amplifier given below is [Marks 1] CF Cc C (c) c CF Solution Ans: (c) (a) −CF Cc −Cc (d) CF (b) Scan to download app to watch free special classes: Q16. Analog Electronics: The O/P impedance of Non ideal op-Amp is donated by Zout The variation in the magnitudes of Zout with increasing frequency of in the circuit shown in below is best represented by (a) (b) [Marks 1] (c) (d) Solution Ans: (a) Q17 Analog Electronics: The steady state output (Vout) of the ckt show below (a) become equal to 0.1 V Scan to download app to watch free special classes: (b) Saturate to +VDD (c) Saturated to – VEE (d) become equal to – 0.1 V [Marks 1] Solution Ans: (c) Q.18 Power system: A 20 MVA, 11.2kV, 4-pole, 50Hz alternator has an inertia constant of 15MJ/MVA. If the input and output power of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s2 is __________. (Round off to nearest integer). [Marks 2] Solution Ans: (75) Q.19 Signal & System: Let an input x(t) = 2sin (10πt ) +5cos (15πt ) +7sin ( 42πt ) +4cos ( 45πt ) is passed through an LTI system having an impulse response sin (10πt ) h ( t ) =2 cos ( 40πt ) πt The output of the system is [Marks 2] Solution Ans: (𝟕 𝐬𝐢𝐧(𝟒𝟐𝝅𝒕) + 𝟒𝐜𝐨𝐬(𝟒𝟓𝛑𝐭)) Q.20 Signal & system: The transfer function of a real system H(S) is given as H ( S) = are positive constants, The system cannot operate as (a) HPF (b) LPF (c) BPF (d) Integrator As+B where, A, B, C, D s +Cs+D 2 [Marks 1] Solution Ans: (a) Q21. Digital Electronics: The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flop, with each flip-flop having a propagation delay of 20ns, is ____________. [Marks 1] Solution Ans: (12.5 MHz) Q22. Signal & system: Consider the signal system as shown below Scan to download app to watch free special classes: Where Y ( t ) =x ( e t ) system is ____ [Marks 1] (a) linear & causal (b) non-linear & causal (c) Non-linear & non causal (d) Linear & non-causal Solution Ans: (d) Q23. Digital Electronics: A MOD 2 and a MOD 5 up counter when cascaded together results in a MOD __________ counter. [Marks 1] Solution Ans: (10) Q24. Power system: Which relay protects from loss of excitation of alternator? (a) Mho relay (b) Directional relay (c) Over current relay (d) Buchholz relay [Marks 1] Solution Ans: (a) Q25. Electromagnetic Fields: If the magnetic field intensity (H) in a conducting region is given by the expression H=x 2 a x +x 2 y 2a y +x 2 y 2 z 2a z A/m. The magnitude of current density, in A/ m2 at x = 1m, y = 2m & z = 1m is __________. (a) 20 (b) 8 (c) 16 (d) 12 [Marks 1] Solution Ans: (d) Q26. Power Systems: If only 5% of the supplied power to a cable reaches the output terminal the power loss in the cable, in decibels is ________ (round off the nearest integer) [Marks 1] Solution Ans: (–0.22) Scan to download app to watch free special classes: Scan to download app to watch free special classes: Q. 27 Power System: The valid positive negative and zero sequence impedance, respectively for a 220 kV, fully transposed three phase transmission line from the given choices are (a) 0.15, 0.15 and 0.35 [Marks 1] (b) 0.2, 0.2 and 0.2 (c) 1.1, 0.15 and 0.08 (d) 0.1, 0.3 and 0.1 Solution Ans: (a) Q28. Electromagnetic Fields: A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is J=J a r 3a z for the region r < b where r is the distance (H) for the region inside the conductor (i.e. r < b) is ________ J (a) a r 3 [Marks 1] 3 J (b) a r 4 5 J (c) a r 3 J (d) a r 4 4 Solution Ans: (b) Q29. Signals and Systems: A Discrete time Fourier series representation of signal x(n) with period m is written as N-1 x ( n ) = a k e j( 2knπ/m ) A discrete time period signal with period N = 3 has the non – zero k=0 Fourier coefficients a -3 = 2 and a 4 = 1 . The signal is (a) 2 + 2e -j2π n 6 j2π n 6 2π cos n 6 j2π n 6 2π cos n 6 j2π n 3 2π cos n 6 (b) 1 + 2e (c) 2 + 2e (d) 1 + 2e 2π cos n 6 Solution Ans: (b) Scan to download app to watch free special classes: [Marks 2] Q30. Control Systems: 1 G (s) = s ( s + 1) Find encirclement of (-1, 0) (a) 1 (b) 3 (c) 2 (d) 0 Solution Ans: (a) [Marks 1] Q31. Measurements: A balanced Wheatstone bridge ABCD has following arm resistance: RAB = 1k + 2.1% RBC = 100 0 5% RCD is unknown resistance RDA = 300 0.4% . The value of RCD its accuracy is (a) 30 0.9 (b) 3000 90 (c) 3000 3 (d) 30 3 [Marks 1] Solution Ans: (d) Q32. Control Systems: The steady state output of the systems to input of the system 100 G (s) = 2 s + 0.19 + 100 y ( t ) = a + b sin (10t + ) r ( t ) = 1 + 0.1sin10t a = 100 b =1 a = 10 (c) b =1 (a) [Marks 2] a =1 b = 10 a =1 (d) b = 100 (b) Solution Ans: (b) Scan to download app to watch free special classes: Q33. Electrical machines: Rotor current frequency given as 1Hz and stator current frequency if 40Hz, find out the speed of induction motor having 8 poles. [Marks 1] Solution Ans: (585 rpm) Q34. Electrical Circuits: Find 𝑉1 across 8kΩ resistance. [Marks 2] Solution Ans: (100V) Q35. Electrical Measurements: A 3–ϕ, 50Hz, circuit is operating, with z1 = (18 + j24 ) and z2 = ( 6 + j8 ) . Find the current through the circuit. [Marks 2] Solution Ans: (20A) Q36. Control Systems: The O.L.T.F of a unity gain negative feedback system has G ( s ) = for which the system is stable is (a) k < 5 (b) k < 3 (c) k > 5 (d) k >3 Solution Ans: (c) Scan to download app to watch free special classes: k . The range of k s + 4s − 5 2 [Marks 1] Q37. Control Systems: A 4-pole induction motor with inertial of 0.1 kg-m2 drives a constant load torque of 2 Nm. The speed of the motor is increased linearly form 1000 rpm to 1500 rpm in 4 second as shown in the figure below, neglect losses in the motor. The energy in joules, consumed by the motor during the speed change is __________. (Round oof to nearest integer) [Marks 2] Solution Ans: (1047.19 J) Q38. Control Systems: The damping ratio and undamped frequency of a closed loop system as below. (a) = 0.707, n = 10 rad/s [Marks 2] (b) = 0.707, n = 100 rad/s (c) = 0.1, n = 10 rad/s (d) = 0.5, n = 10 rad/s Solution Ans: (d) Q39. Electrical Circuits: The network shown has resonant frequency of 150Hz and B.W = 600Hz. The Q-factor is ______. [Marks 1] Solution Ans: (250) Q40. Electrical Circuits: An inductor having Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of circuit is ______. [Marks 1] Solution Ans: (48) Scan to download app to watch free special classes: Scan to download app to watch free special classes: Scan Now for Upcoming Batches Scan to download app to watch free special classes: Q41. Electrical Circuits: In the circuit shown below the switch S is closed at t = 0. The magnitude of steady state voltage in volts across the 6Ω resistor is ________. (Round of to decimal place). [Marks 1] Solution Ans: (5V) Q42. Electrical Machines: A 3 – ϕ, 415V, 50Hz I.M, draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of rated current using a 3 – ϕ auto transformer neglect all losses, find transformation ratio of autotransformer _________. [Marks 1] Solution Ans: (0.632) Q43. Electrical Machines: A 280V, separately excited DC motor with armature resistance Ra = 1Ω and constant field excitation drives a load. load torque (TL) ∝ speed. Motor draws a current of 30A when running at a speed 1000 rpm. Neglect frictional loss. What will be speed (in rpm) when additional resistance (𝑅𝑒𝑥𝑡 ) = 10Ω connected in series __________. [Marks 2] Solution Ans: (482.76) Q44. Electrical Machines: A star connected 3 – ϕ, 400V, 50 kVA, 50Hz synchronous motor has synchronous reactance = 1Ω /ph with negligible Ra. The shaft load of motor is 10 kW, while the power factor is 0.8 leading. The loss in motor is 2kW. The magnitude of per phase excitation Emf ________. [Marks 2] Solution Ans: (244.54) Q45. Electrical Machines: The type of 1 – ϕ I.M expected to have the maximum power factor during steady state running condition Scan to download app to watch free special classes: (a) Shaded pole (b) Split phase (resistance start) (c) Capacitor start (d) Capacitor start and capacitor run. [Marks 1] Solution Ans: (d) Q46. Control Systems: Let a causal LTI signal system be governed by the following differential equation 1 dy y (t ) + = 2 x ( t ) where x(t) and y(t) are the input and out respectively its impulse 4 dt response is (a) 8e 1 − t 4 u (t ) 1 − t 4 u (t ) (b) 2e (c) 8e −4t u ( t ) (d) 2e−4t u ( t ) [Marks 1] Solution Ans: (c) Q47. Electrical Machines: Consider an ideal full-bridge single phase DC-AC inverter with a DC bus voltage magnitude of 1000V. The inverter output voltage v(t) shown below, is obtained when diagonal switches of the inverter are switched with 50% duty cycle. The inverter feeds a load with a sinusoidal 2 current given by, i ( t ) = 10sin t − A , where = . The active power in watts, T 3 delivered to the load is ________. (Rounded off to nearest integer) [Marks 2] Solution Ans: (3183.09) Q48. Control Systems: The bode magnitude plot of a first order stable single system is constant with frequency, the asymptotic value of the high frequency phase, for the signal system is –180° the signal system has Scan to download app to watch free special classes: (a) One LHP pole, 1 LHP zero at the same frequency (b) 2 RHP poles, 1 LHP zero (c) 1 LHP pole and 1 RHP zero at the same frequency (d) Two LHP pole and 1 RHP zero [Marks 2] Solution Ans: (c) Q49. Power Electronics: For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is I dc = 15A and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude of the fundamental component of the source current, the amperes, is ________. (Rounded off to two decimal places) [Marks 2] Solution Ans: (17.65A) Q50. Power System: A 3-pahse grid-connected voltage source converter with DC link voltage of 1000V is switched using sinusoidal pulse width modulation (PWM) technique. If the grid phase current is 10A and the 3-phase complex power supplied by the converted is given by (–4000–j3000) VA, then the modulation index used is sinusoidal PWM is _______. (Rounded off to two decimal places) [Marks 2] Solution Ans: (0.4714) Q51. Power System: The GMR of the bundle conductors given below is _______ r. [Marks 1] Solution Ans: (1.723) Scan to download app to watch free special classes: Scan to download app to watch free special classes: