GATE –Past papers ELECTRICAL ENGINEERING - UNSOLVED PAPER - 2010

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

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01 The value of the quantity P, where P = , is equal to 0 1 e 1/e Problem

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Problem 02 Divergence of the three-dimensional radial vector field is 3 1/r + + 3( + + )

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Problem 03 The period of the signal x(t) = 8 sin(0.8 π t + ( π /4)) is 0.4 π s 0.8 π s 1.25s 2.5s

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Problem 04 The system represented by the input-output relationship y(t) t > 0 is Linear and causal Linear but not causal Causal but not linear Neither linear nor causal

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Problem 05 The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0 + , the current through the 1 μ F capacitor is OA 1 A 1.25A 5A

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Problem 06 The second harmonic component of the periodic waveform given in the figure has an 0 1 2/ π √5

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Problem 07 As shown in the figure, a 1 Ω resistance is connected across a source that has a load line v + i = 100. The current through the resistance is 25A 50A 100A 200A

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Problem 08 A wattmeter is connected as shown in the figure. The wattmeter reads Zero always Total power consumed by Z 1 and Z 2 Power consumed by Z 1 Power consumed by Z 2

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Problem 09 An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2 Ω order to change the range to 0 - 25 A, we need to add a resistance of 0.8 Ω in series with the meter 1.0 Ω in series with the meter 0.04 Ω in parallel with the meter 0.05 Ω in parallel with the meter

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Problem 10 As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately: 10 ± 1% 10 ± 2% 10 ± 5% 10 ± 10%

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Problem 11 For the system 2/(s + 1), the approximate time taken for a step response to reach 98% of its final value is 1s 2s 4s 8s

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Problem 12 If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then A, B are resistances and C, D capacitances A, C are resistances and B, D capacitances A, B are capacitances and C, D resistances A, C are capacitances and B, D resistances

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Problem 13 A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1A, and the secondary current is 1A. If core losses and leakage reactance's are neglected, the primary current is 1.41A 2A 2.24A 3A

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Problem 14 Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltages V AB and V CD are as indicated in the figure, and I > 0, then V AB <0, V CD < 0, V AB > V CD V AB > 0, V CD > 0, V AB > V CD V AB > 0, V CD > 0, V AB < V CD V AB > 0, V CD < 0

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Problem 15 A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by r s , r r , x s , x r and X m , respectively. The magnitude of the starting current of the motor is given by b. c. d.

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Problem 16 Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is -1pu 1 pu 2pu 3pu

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Problem 17 Consider two buses connected by an impedance of (0 + j5) Ω . The bus 1 voltage is 100 30 º V, and bus 2 voltage is 100 0 º . The real and reactive power supplied by bus 1, respectively, are 1000W, 268VAr -1000W, -134Var 276.9W, -56.7Var -276.9W, 56.7Var

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Problem 18 A three-phase, 33kVoil circuit breaker is rated 1200A, 2000MVA, 3s. The symmetrical breaking current is 1200 A 3600 A 35 kA 104.8 kA

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Problem 19 Consider a stator winding of an alternator with an internal high-resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio 400/5 A as shown. The current through the operating coil is 0.17875 A 0.2 A 0.375 A 60 kA

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Problem 20 The zero-sequence circuit of the three phase transformer shown in the figure is a. b. c. d.

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Problem 21 Given that the op-amp is ideal, the output voltage V 0 is 4V 6V 7.5V 12.12V

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Problem 22 Assuming that the diodes in the given circuit are ideal, the voltage V 0 is 4V 5V 7.5V 12.12V

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Problem 23 The power electronic converter shown in the figure has a single-pole double-throw switch. The pole P of the switch is connected alternately to throws A and B. The converter shown is a step-down chopper (buck converter) half-wave rectifier step-up chopper (boost converter) full-wave rectifier

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Problem 24 Figure shows a composite switch consisting of a power transistor (BJT) in series with a diode. Assuming that the transistor switch and the diode are ideal, the l-V characteristic of the composite switch is b. d.

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Problem 25 The fully controlled thyristor converter in the figure is fed from a single-phase source. When the firing angle is 0°, the dc output voltage of the converter is 300 V. What will be the output voltage for a firing angle of 60°, assuming continuous conduction ? 150V 210V 300V 10O π V

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Problem 26 At t = 0, the function f(t) = ((sin t)/t) has a minimum a discontinuity a point of inflection a maximum

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Problem 27 A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is 1/3 3/7 1/2 4/7

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Problem 28 An eigenvector of P = is : [-1 1 1] T [1 2 1] T [1 -1 2] t [2 1 -1] T

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Problem 29 For the differential equation - with initial conditions x(0) = 1 and , the solution is x(t) = 2e -6t - e -2t x(t) = 2e -2t - e -4t x(t) = -e -6t + 2e -4t x(t) = e -2t + 2e -4t

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Problem 30 For the set of equations, x 1 + 2x 2 + x 3 + 4x 4 =2 and 3x 1 + 6x 2 + 3x 2 + 12x 4 = 6. The following statement is true Only the trivial solution x 1 = x 2 = x 3 = x 4 = 0 exists There are no solutions A unique non-trivial solution exists Multiple non-trivial solutions exist

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Problem 31 x(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown in the figure. The value of {where X( ω ) is the Fourier transform of x(t)} is 2 2 π 4 4 π

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Problem 32 Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is h[n]= {1,0,0,1} h[n]= {1,0,1} h[n]= {1,1,1,1} h[n]= {1,1,1}

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Problem 33 If the 12 Ω resistor draws a current of 1A as shown in the figure, the value of resistance R is 4 Ω 6 Ω 8 Ω 18 Ω

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Problem 34 The two-port network P shown in the figure has ports 1 and 2, denoted by terminals (a, b) and (c, d), respectively. It has an impedance matrix Z with parameters denoted by z ij . A 1 Ω resistor is connected in series with the network at port 1 as shown in the figure. The impedance matrix of the modified two-port network (shown as a dashed box) is a. b. c. d.

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Problem 35 The Maxwell's bridge shown in the figure is at balance. The parameters of the inductive coil are R = R 2 R 3 /R 4 , L = C 4 R 2 R 3 L = R 2 R 3 /R 4 , R = C 4 R 2 R 3 R = R 4 /R 2 R 3 , L = 1 (C 4 R 2 R 3 ) L = R 4 /R 2 R 3 , R = 1(C 4 R 2 R 3 )

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Problem 36 The frequency response of G(s) = 1/[s(s + 1)(s + 2)] plotted in the complex G(j ω ) plane (for 0 < ω < ) is a. b. c. d.

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Problem 37 The system = Ax + Bu with A = , B = is stable and controllable stable but uncontrollable unstable but controllable unstable and uncontrollable

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Problem 38 The characteristic equation of a closed-loop system is s(s + 1)(s + 3) + k(s + 2) = 0, k > 0. Which of the following statements is true? Its roots are always real It cannot have a breakaway point in the range -1 < Re[s] < 0 Two of its roots tend to infinity along the asymptotes Re[s] = -1 It may have complex roots in the right half plane

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Problem 39 A 50 Hz synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator ? The magnitude of terminal voltage decreases, and the field current does not change The magnitude of terminal voltage increases, and the field current does not change The magnitude of terminal voltage increases, and the field current increases The magnitude of terminal voltage does not change, and the field current decreases

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Problem 40 A separately excited dc machine is coupled to a 50Hz, three-phase, 4-pole induction machine as shown in the figure. The dc machine is energized first and the machines rotate at 1600 rpm. Subsequently the induction machine is also connected to a 50Hz, three-phase source, the phase sequence being consistent with the direction of rotation. In steady state, Both machines act as generators The dc machine acts as a generator, and the induction machine acts as a motor The dc machine acts as a motor, and the induction machine acts as a generator Both machines act as motors

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Problem 41 A balanced star-connected and purely resistive load is connected at the secondary of a star-delta transformer as shown in the figure. The line-to-line voltage rating of the transformer is 110V/220V. Neglecting the non-idealities of the transformer, the impedance 'Z' of the equivalent star-connected load, referred to the primary side of the transformer, is (3+j0) Ω (0.866 - j0.5) Ω (0.866 + j0.5) Ω (1+ j0) Ω

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Problem 42 Consider a three-phase, 50Hz, 11 kV distribution system. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The self capacitance of the insulator is 5 times the shunt capacitance between the link and the ground, as shown in the figure. The voltage across the two insulators is e1 = 3.74kV, e2 = 2.61 kV e1 = 3.46kV, e2 = 2.89kV e1 = 6.0kV, e2 = 4.23kV e1 = 5.5kV, e2 = 5.5kV

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Problem 43 Consider a three-core, three-phase, 50Hz, 11 kV cable whose conductors are denoted as R, Y and B in the figure. The inter-phase capacitance (C1) between each pair of conductorqalis the capacitance between each line conductor and the sheath is 0.4 μ F. The per-phase charging current is 2.0A 2.4A 2.7A 3.5A

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Problem 44 For the power system shown in the figure below, the specifications of the components are the following : G1: 25 kV, 100 MVA, X = 9% G2: 25 kV, 100MVA, X = 9% T1: 25 kV/220 kV, 90 MVA, X = 12% T2: 220 kV/25 kV, 90 MVA, X = 12% Line1: 220 kV, X = 150 ohms Choose 25 kV as the base voltage at the generator G1, and 200 MVA as the MVA base. The impedance diagram is

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a. b. c. d.

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Problem 45 The transistor circuit shown uses a silicon transistor with V BE = 0.7 V, I C I E and a dc current gain of 100. The value of V 0 is 4.65A 5V 6.3V 7.23V

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Problem 46 The TTL circuit shown in the figure is fed with the waveform X (also shown). All gates have equal propagation delay of 10 ns. The output Y of the circuit is a. b. c. d.

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Problem 47 When a "CALL Addr " instruction is executed, the CPU carries out the following sequential operations internally: Note: (R) means content of register R ((R)) means content of memory location pointed to by R PC means Program Counter SP means Stack Pointer a. (SP) incremented (PC) Addr ((SP)) (PC) b. (PC) Addr ((SP)) (PC) (SP) incremented

Directions for question 48 to 49: Common Data Questions:

Directions for question 48 to 49: Common Data Questions A separately excited DC ,motor runs at 1500 rpm under no – load with 200 V applied to the armature the field voltage is maintained at its rated value. The speed of the motor, when it delivers a torque of 5 Nm, is 14000 rpm as shown in the figure. The rotational losses and armature reaction are neglected.

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Problem 48 The armature resistance of the motor is, 2 Ω 3.4 Ω 4.4 Ω 7.7 Ω

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Problem 49 For the motor to deliver a torque of 2.5 Nm at 1400 rpm the armature voltage to be applied is 125.5V 193.3V 200V 241.7V

Directions for question 50 to 51: Common Data Questions:

Directions for question 50 to 51: Common Data Questions Given f (t) and g (t) as shown below :

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Problem 50 g(t)can be expressed as g(t)=f(2t-3) g(t) = f((t/2) - 3) g(t) = f(2t - (3/2)) g(t) = f((t/2) - (3/2))

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Problem 51 The Laplace transform of g(t) is (1/s)(e 3s - e 5s ) (1/s)(e" 5s - e" 3s ) (e" 3s /s)(1 - e" 2s ) (1/s)(e 5s - e 3s )

Directions for question 52 to 53: Common Data Questions:

Directions for question 52 to 53: Common Data Questions The following Karnaugh map represents a function F.

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Problem 52 A minimized form of the function F is F = Y + YZ F = + YZ F = + Y F = + Z

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Problem 53 Which of the following circuits is a realization of the above function F? a. b. c. d.

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The L – C circuit shown in the figure has an inductance L= 1 m H and a Capacitance C = 10 u F

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Problem 54 The initial current through the inductor is zero, while the initial capacitor voltage is 100 V. The switch is closed at t = 0. The current i through the circuit is: 5 cos (5 x 10 3 t)A 5 sin (10 4 t)A 10 cos (5 x 10 3 t)A 10 sin (10 4 t)A

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Problem 55 The L-C circuit of (above question) is used to commutate a thyristor , which is initially carrying a current of 5A as shown in the figure below. The values and initial conditions of L and C are the same as in (above question). The switch is closed at t = 0. If the forward drop is negligible, the time taken for the device to turn off is 52 μ s 156 μ s 312 μ s 26 μ s

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Problem 56 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is 2 17 13 3

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Problem 57 The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed : Worker fallow : land unaware : sleeper wit: jester renovated : house

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Problem 58 Choose the most appropriate word from the options given below to complete the following sentence If we manage to _______ our natural resources, we would leave a better planet for our children. uphold restrain cherish conserve

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Problem 59 Which of the following options is closest in meaning to the word: Circuitous ? cyclic indirect confusing crooked

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Problem 60 Choose the most appropriate word from the options given below to the complete the following sentence: His rather casual remarks on politics ________his lack of seriousness about the subject. masked belied betrayed suppressed

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Problem 61 Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts: Hari's age + Gita's age > Irfan's age + Saira's age. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest. There are no twins. In what order were they born (oldest first) ? HSIG SGHI IGSH IHSG

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Problem 62 5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall? 20 18 16 15

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Problem 63 Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the above passage: Modern warfare has resulted in civil strife. Chemical agents are useful in modern warfare. Use of chemical agents in warfare would be undesirable. People in military establishments like to use chemical agents in war.

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Problem 64 Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed? 50 51 52 54

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Problem 65 If 137 + 276 = 435 how much is 731 + 672? 534 1403 1623 1513

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