# Electrical Engineering - unsolved - 2009

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### GATE –Past papers:

GATE –Past papers ELECTRICAL ENGINEERING - UNSOLVED PAPER - 2009

### SECTION – I :

SECTION – I Single Correct Answer Type There are five parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate

### Problem:

01 The pressure coil of a dynamometer type wattmeter is highly inductive highly resistive purely resistive purely inductive Problem

### Problem:

Problem 02 The measurement system shown in the figure uses three sub-systems in cascade whose gains are specified as G 1 , G 2 and (I/G 3 ). The relative small errors associated with each respective subsystem G 1 , G 2 and G 3 are 1 , 2 and 3 .The error associated with the output is: 1 + 2 + (1/ 3 ) (( 1 . 2 )/ 3 ) 1 + 2 - 3 1 + 2 + 3

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Problem 03 The following circuit has a source voltage V s as shown in the graph. The current through the circuit is also shown. The element connected between a and b could be b. c. d.

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Problem 04 The two inputs of a CRO are fed with two stationary periodic signals. In the X-Y mode, the screen shows a figure which changes from ellipse to circle and back to ellipse with its major axis changing orientation slowly and repeatedly. The following inference can be made from this. The signals are not sinusoidal The amplitudes of the signals are very close but not equal The signals are sinusoidal with their frequencies very close but not equal There is a constant but small phase difference between the signals

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Problem 05 The increasing order of speed of data access for the following devices is Cache Memory CDROM Dynamic RAM Processor Registers Magnetic Tape (v), (ii), (iii), (iv), ( i ) (v), (ii), (iii), ( i ), (iv) (ii), ( i ), (iii), (iv), (v) (v), (ii), ( i ), (iii), (iv)

### Problem:

Problem 06 A field excitation of 20 A in a certain alternator results in an armature current of 400A in short circuit and a terminal voltage of 2000V on open circuit. The magnitude of the internal voltage drop within the machine at a load current of 200A is 1V 10V 100V 1000V

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Problem 07 The current through the 2 k Ω resistance in the circuit shown is 0mA 1mA 2mA 6mA

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Problem 08 Out of the following plant categories Nuclear Run-of-river Pump Storage Diesel The base load power plants are ( i ) and (ii) (ii) and (iii) ( i ), (ii) and (iv) ( i ), (iii) and (iv)

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Problem 09 For a fixed value of complex power flow in a transmission line having a sending end voltage V, the real power loss will be proportional to V V 2 1/V 2 1/V

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Problem 10 How many 200W/220V incandescent lamps connected in series would consume the same total power as a single 100W/220V incandescent lamp? not possible 4 3 2

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Problem 11 A Linear Time Invariant system with an impulse response h(t) produces output y(t) when input x(t) is applied. When the input x (t ) is applied to a system with impulse response h(t ), the output will be y(t) y(2(t - )) y(t - ) y(t - 2 )

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Problem 12 The nature of feedback in the opamp circuit shown is Current - Current feedback Voltage - Voltage feedback Current - Voltage feedback Voltage - Current feedback

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Problem 13 The complete set of only those Logic Gates designated as Universal Gates is NOT, OR and AND Gates XNOR, NOR and NAND Gate NOR and NAND Gates XOR, NOR and NAND Gates

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Problem 14 The single phase, 50Hz, iron core transformer in the circuit has both the vertical arms of cross sectional area 20cm 2 and both the horizontal arms of cross sectional area 10cm 2 . If the two windings shown were wound instead on opposite horizontal arms, the mutual inductance will double remain same be halved become one quarter

### Problem:

Problem 15 A 3-phase squirrel cage induction motor supplied from a balanced 3-phase source drives a mechanical load. The torque-speed characteristics of the motor (solid curve) and of the load (dotted curve) are shown. Of the two equilibrium points A and B, which of the following options correctly describes the stability of A and B? A is stable B is unstable A is unstable B is stable Both are stable Both are unstable

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Problem 16 An SCR is considered to be a semi-controlled device because it can be turned OFF but not ON with a gate pulse it conducts only during one half-cycle of an alternating current wave it can be turned ON but not OFF with a gate pulse it can be turned ON only during one half-cycle of an alternating voltage wave

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Problem 17 The polar plot of an open loop stable system is shown below. The closed loop system is Always stable Marginally stable Unstable with one pole on the RH s-plane Unstable with two poles on the RH s-plane

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Problem 18 The first two rows of Routh's tabulation of a third order equation are as follows. S 3 2 2 S 2 4 4 . This means there are two roots at s = ±j and one root in right half s-plane two roots at s = ±j2 and one root in left half s-plane two roots at s = ±j2 and one root in right half s-plane two roots at s = ±j and one root in left half s-plane

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Problem 19 The asymptotic approximation of the log-magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function is d.

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Problem 20 The trace and determinant of a 2 x 2 matrix are known to be -2 and -35 respectively. Its eigen values are -30 and -5 -37 and -1 -7 and 5 17.5 and -2

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Problem 21 The following circuit has R = 10 Ω , C = 10 μ F R. The input voltage is a sinusoid at 50Hz with an rms value of 10V. Under ideal conditions, the current i s from the source is 10 π mA leading by 90° 20 π mA leading by 90° 10 mA leading by 90° 10 π mA lagging by 90°

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Problem 22 In the figure shown, all elements used are ideal. For time t < 0, S 1 remained closed and S 2 open. At t = 0, S 1 is opened and S 2 is closed. If the voltage V c2 across the capacitor C 2 at t = 0 is zero, the voltage across the capacitor combination at t = 0 + will be 1V 2V 1.5V 3V

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Problem 23 Transformer and emitter follower can both be used for impedance matching at the output of an audio amplifier. The basic relationship between the input power P jn and output power P out in both the cases is P in = P out for both transformer and emitter follower P in > P out for both transformer and emitter follower P in < P out for transformer and P jn = P 0ut for emitter follower P in = P out for transformer and P jn < P out for emitter follower

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Problem 24 The equivalent capacitance of the input loop of the circuit shown is 2 μ F 100 μ F 200 μ F 4 μ F

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Problem 25 In an 8085 microprocessor, the contents of the Accumulator, after the following instructions are executed will become XRA A MVIB FOH SUB B 01 H OF H F0 H 10 H

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Problem 26 For the Y-bus matrix of a 4-bus system given in per unit, the buses having shunt elements are Y BUS = J 3 and 4 2 and 3 1 and 2 1, 2 and 4

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Problem 27 The unit-step response of a unity feedback system with open loop transfer function G(s) = K/((s + I) (s + 2)) is shown in the figure. The value of K is 0.5 2 4 6

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Problem 28 The open loop transfer function of a unity feedback system is given by G (s) = (e -0.1s )/ s. The gain margin of this system is 11.95dB 17.67dB 21.33dB 23.9dB

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Problem 29 Match the items in List-I with the items in List- ll and select the correct answer using the codes given below the lists. A 2, b 3, c 4, d 1 a 2, b 4, c 3, d 1 a 4, b 3, c 1, d 2 A 4, b 1, c 3, d 2 List-I To List- ll Use a improve power factor 1 shunt reactor b reduce the current ripples 2 shunt capacitor c increase the power flow in line 3 series capacitor d reduce the Ferranti effect 4 series reactor

### Problem:

Problem 30 Match the items in List-I with the items in List- ll and select the correct answer using the codes given below the lists. a 2, b 1, c 3, a 3, b 2, c 1 a 1, b 2, c 3 a 1, b 3, c 2 List I Type of transmission line List ll Type of distance relay preferred a Short Line 1 Ohm Relay b Medium Line 2 Reactance Relay c Long Line 3 Mho Relay

### Problem:

Problem 31 Three generators are feeding a load of 100 MW. The details of the generators are In the event of increased load power demand, which of the following will happen? All the generators will share equal power Generator-3 will share more power compared to Generator-1 Generator-1 will share more power compared to Generator-2 Generator-2 will share more power compared to Generator-3 Rating (MW) Efficiency (%) Regulation ( p.u .) on 100 MVA base Generator-1 100 20 0.02 Generator-2 100 30 0.04 Generator -3 100 40 0.03

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Problem 32 A 500MW, 21 kV, 50Hz, 3-phase, 2-pole synchronous generator having a rated p.f = 0.9, has a moment of inertia of 27.5 x 10 3 kg-m 2 . The inertia constant (H) will be 2.44s 2.71s 4.88s 5.42s

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Problem 33 f(x, y) is a continuous function defined over (x, y) Є [0, 1] × [0, 1], Given the two constraints, x > y 2 and y > x 2 , the volume under f(x, y) is a. b. c. d.

### Problem:

Problem 34 Assume for simplicity that N people, all born in April (a month of 30 days), are collected in a room. Consider the event of at least two people in the room being born on the same date of the month, even if in different years, e.g. 1980 and 1985. What is the smallest N so that the probability of this event exceeds 0.5? 20 7 15 16

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Problem 35 A cascade of 3 Linear Time Invariant systems is causal and unstable. From this, we conclude that Each system in the cascade is individually causal and unstable At least one system is unstable and at least one system is causal At least one system is causal and all systems are unstable The majority are unstable and the majority are causal

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Problem 36 The Fourier Series coefficient, of a periodic signal x(t), expressed as x(t) = are given by A -2 = 2 - j1; a -1 = 0.5 + j0.2; a 0 = j2; a 1 = 0.5 - j0.2; a 2 = 2 + j1; and a k = 0; for |k| > 2. Which of the following is true? x(t) has finite energy because only finitely many coefficients are non-zero x(t) has zero average value because it is periodic The imaginary part of x(t) is constant The real part of x(t) is even

### Problem:

Problem 37 The z-transform of a signal x[n] is given by 4z -3 + 3z -1 + 2 - 6z 2 + 2z 3 . It is applied to a system, with a transfer function H (z) = 3z -1 - 2. Let the output be y(n). Which of the following is true? y(n) is non causal with finite support y(n) is causal with infinite support y(n) = 0; |n| > 3 Re [Y (z)] z = = - Re [Y (z)] z= ; lm [Y (z)] z= =| m [Y (z)] z = ; -

### Problem:

Problem 38 A cubic polynomial with real coefficients can possibly have no extrema and no zero crossings may have up to three extrema and up to 2 zero crossings cannot have more than two extrema and more than three zero crossings will always have an equal number of extrema and zero crossings

### Problem:

Problem 39 Let x 2 - 117 = 0. The iterative steps for the solution using Newton - Raphson's method is given by x k +1 = (1/2)( x k + (117/ x k )) x k + 1 = x k - (117/ x k ) x k +1 = x k - ( x k /117) x k + 1 = x k - (1/2) ( x k + (117/ x k ))

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Problem 40 F (x, y) = (x 2 + xy ) x + (y 2 + xy ) y . It's line integral over the straight line from (x, y) = (0, 2) to (x, y) = (2, 0) evaluates to -8 4 8 0

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Problem 41 An ideal opamp circuit and its input waveform are shown in the figures. The output waveform of this circuit will be a. b. c. d.

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Problem 42 A 220V, 50Hz, single-phase induction motor has the following connection diagram and winding orientations shown. MM' is the axis of the main stator winding (M 1 M 2 ) and AA' is that of the auxiliary winding (A 1 A 2 ). Directions of the winding axes indicate direction of flux when currents in the windings are in the directions shown. Parameters of each winding are indicated. When switch S is closed, the motor rotates clockwise rotates anticlockwise does not rotate rotates momentarily and comes to a halt

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Problem 43 The circuit shows an ideal diode connected to a pure inductor and is connected to a purely sinusoidal 50Hz voltage source. Under ideal conditions the current waveform through the inductor will look like a. b. c. d.

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Problem 44 The Current Source Inverter shown in figure, is operated by alternately turning on thyristor pairs (T 1 , T 2 ) and (T 3 , T 4 ). If the load is purely resistive, the theoretical maximum output frequency obtainable will be 125kHz 250kHz 500kHz 50kHz

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Problem 45 In the chopper circuit shown, the main thyristor ( T M ) is operated at a duty ratio of 0.8, which is much larger the commutation interval. If the maximum allowable reapplied dv / dt on T M is 50 V/ μ s, what should be the theoretical minimum value of C 1 ? Assume current ripple through L 0 to be negligible. 0.2 μ F 0.02 μ F 2 μ F 20 μ F

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Problem 46 Match the switch arrangements on the top row to the steady-state V-l characteristics on the lower row. The steady state operating points are shown by large black dots A- I, B - II, C - III, D - IV A - II, B - IV, C – I, C - III A - IV, B - III, C - I, D - II A – VI, B - III, C - II, D - I

### Problem:

Problem 47 For the circuit shown, find out the current flowing through the Ω resistance. Also identify the changes to be made to double the current through the 20 Ω resistance (5A; Put V s = 20V) (2A; Put V s = 8V) (5A; Put Is = 10A) (7A; Put Is = 12A)

### Problem:

Problem 48 The figure shows a three-phase delta connected load supplied from a 400V, 50 Hz, 3-phase balanced source. The pressure coil (PC) and current coil (CC) of a wattmeter are connected to the load as shown, with the coil polarities suitably selected to ensure a positive deflection. The wattmeter reading will be 0 1600 Watt 800 Watt 400 Watt

### Problem:

Problem 49 An average-reading digital multimeter reads 10V when fed with a triangular wave, symmetric about the time-axis. For the same input an rms -reading meter will read. 2 O/ √ 3 10/ √ 3 20 √ 3 10 √ 3

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Problem 50 Figure shows the extended view of a 2 pole dc machine with 10 armature conductors. Normal brush positions are shown by A and B, placed at the interpolar axis. If the brushes are now shifted, in the direction of rotation, to A' and B' as shown, the voltage waveform V A'B' will resemble a. b. c. d.

### PowerPoint Presentation:

The star- delta transformer shown above is excited on the star side with a balanced , 4 –wire ,3 phase , sinusoidal voltage supply of rated magnitude . The transformer is under no load condition.

### Problem:

Problem 51 With both S1 and S2 open, the core flux waveform will be A sinusoid at fundamental frequency Flat topped with third harmonic Peaky with third harmonic None of these

### Problem:

Problem 52 With S2 closed and S1 open, the current waveform in the delta winding will be a sinusoid at fundamental frequency flat topped with third harmonic only third harmonic None of these

### PowerPoint Presentation:

The circuit diagram shows a two winding, lossless transformer with no leakage Flux, excited from a current source, i (t) whose waveform is also shown The transformer has a magnetizing inductance of 400/ mh

### Problem:

Problem 53 The peak voltage across A and B, with S open is 400/ π V 800V 4000/ π V 800/ π V

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Problem 54 If the waveform of i (t) is changed to i (t) = 10 sin (100) A, the peak voltage across A and B with S closed is 400 V 240V 320 V 160 V A system is described by the following state and output equations ((dx 1 (t))/ dt ) = -3x 1 (t)+x 2 (t) + 2u (t) ((dx 2 (t))/ dt ) = - 2x 2 (t) + u (t) V (t) = X 1 (t) where u (t) is the input and y (t) is the output

### Problem:

Problem 55 The system transfer function is (s + 2)/(s 2 + 5s - 6) (s + 3)/(s 2 + 5s + 6) (s + 5)/(s 2 + 5s + 6) (2s - 5)/(s 2 + 5s - 6)

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Problem 56 The state transition matrix of the above system is

### PowerPoint Presentation:

The figure above shows coils 1 and 2 with dot markings as shown , having 4000 and 6000 turns respectively. Both coils have a rated current of 25 A Coil 1 is excited with single phase, 400V, 50 Hz supply

### Problem:

Problem 57 The coils are to be connected to obtain a single phase, 400/1000V, auto transformer to drive a load of 10kVA. Which of the options given should be exercised to realize the required auto transformer? Connect A and D; Common B Connect B and D; Common C Connect A and C; Common B Connect A and C; Common D

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Problem 58 In the autotransformer obtained in above Question, the current in each coil is Coil-1 is 25 A and Coil-2 is 10 A Coil-1 is 10 A and Coil-2 is 25 A Coil-1 is 10 A and Coil-2 is 15 A Coil-1 is 15 A and Coil-2 is 10 A

### Problem:

Problem 59 For the circuit given above, the Thevenin's resistance across the terminals A and B is 0.5k Ω 0.2k Ω 1 K Ω 0.11k Ω

### Problem:

Problem 60 For the circuit given above, the Thevenin's voltage across the terminals A and B is 1.25V 0.25V 1V 0.5V

### PowerPoint Presentation:

FOR SOLUTION VISIT WWW.VASISTA.NET / 