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1 Q. No. 5 Carry One Mark Each GATE question papers: Electrical Engineering 00 (EE) Published by:. The value of the quantity P, where P = xe x dx, is equal to o 0 e /e. Divergence of the threedimensional radial vector field r is 3 /r î ĵ kˆ 3( î ĵ kˆ ) 3. The period of the signal x(t) = 8sin 0.8t is 4 0.4s 0.8s.5s.5s 4. The system represented by the inputoutput relationship y(t) = x( )d,t > 0 is Linear and causal Linear but not causal Causal but not linear Neither linear nor causal 5. 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 F capacitor is 5 Ω t = 0 0A A.5A 5A 6. The second harmonic component of the periodic waveform given in the figure has an amplitude of 0 T/ T 0 / 5 7. As shown in the figure, a Ω resistance is connected across a source that has a load line v i = 00. The current through the resistance is Source v 5A 50A 00A 00A 8. A wattmeter is connected as shown in the figure. The wattmeter reads Current coil Potential coil i Wattmeter Ω μf t 5t 4Ω ero always Total power consumed by and Power consumed by Power consumed by Page of 3

2 GATE question papers: Electrical Engineering 00 (EE) Published by: 9. An ammeter has a current range of 0 5 A, and its internal resistance is 0.Ω. In order to change the range to 0 5 A, we need to add a resistance of 0.8Ω in series with the meter.0ω in series with the meter 0.04Ω in parallel with the meter 0.05Ω in parallel with the meter 0. As shown in the figure, a negative feedback system has an amplifier of gain 00 with ±0% tolerance in the forward path, and an attenuator of value 9/00 in the feedback path. The overall system gain is approximately: 00 ± 0% 0±% 0±% 0±5% 0±0%. For the system (s 9 00, the approximate time taken for a step response to reach 98% of its final ) value is s s 4s 8s. If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then h h A C a Coupled tank b Electrical equivalent A, are resistances and C, D capacitances A, C are resistances and, D capacitances A, are capacitances and C, D resistances A, C are capacitances and, D resistances 3. A singlephase transformer has a turns ratio of :, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is A, and the secondary current is A. If core losses and leakage reactance s are neglected, the primary current is.4a A.4 A 3 A 4. Power is transferred from system A to system by an HDC link as shown in the figure. If the voltages A and CD are as indicated in the figure, and I > 0, then AC System A A A D e ctifier Inverter A <0, CD <0, A > CD A >0, CD >0, A > CD A >0, CD >0, A < CD A >0, CD <0. Power Flow l A CD C D AC System Page of 3

3 GATE question papers: Electrical Engineering 00 (EE) Published by: 5. A balanced threephase voltage is applied to a starconnected induction motor, the phase to neutral voltage being. 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 m, respectively. The magnitude of the starting current of the motor is given by (rs rr ) (x s x r ) (rs (x s x m) (r r ) (x x (r (x x s r m r ) s m r ) 6. Consider a step voltage wave of magnitude pu 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 A e actor pu pu pu 3pu 7. Consider two buses connected by an impedance of (0j5) Ω. The bus voltage is o, and bus voltage is 00 0 o.the real and reactive power supplied by bus, respectively, are 000W, 68Ar 000W, 34ar 76.9W, 56.7ar 76.9W, 56.7ar 8. A threephase, 33k oil circuit breaker is rated 00A, 000MA, 3s. The symmetrical breaking current is 00 A 3600 A 35 ka 04.8 ka 9. Consider a stator winding of an alternator with an internal highresistance 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 CT ratio 400 /5 CT ratio 400 /5 0 j0 A 50 j0 A Operating coil A 0. A 0.375A 60 ka Page 3 of 3

4 0. The zerosequence circuit of the three phase transformer shown in the figure is GATE question papers: Electrical Engineering 00 (EE) Published by: G G r r. Given that the opamp is ideal, the output voltage 0 is Assuming that the diodes in the given circuit are ideal, the voltage 0 is 0kΩ 0 0kΩ 0kΩ The power electronic converter shown in the figure has a singlepole doublethrow switch. The pole P of the switch is connected alternately to throws A and. The converter shown is a A L μ IN G OUT r b y G r r stepdown chopper (buck converter) halfwave rectifier stepup chopper (bost converter) fullwave rectifier Page 4 of 3

5 GATE question papers: Electrical Engineering 00 (EE) Published by: 4. Figure shows a composite switch consisting of a power transistor (JT) in series with a diode. Assuming that the transistor switch and the diode are ideal, the I characteristic of the composite switch is I I 5. The fully controlled thyristor converter in the figure is fed from a singlephase source. When the firing angle is 0, the dc output voltage of the converter is 300. What will be the output voltage for a firing angle of 60, assuming continuous conduction? I I I dc Q. No. 6 5 Carry Two Marks Each 6. sin t At t = 0, the function f(t) = t has a minimum a discontinuity a point of inflection D) a maximum 7. 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 /3 3/7 / 4/ An eigenvector of p = 0 is [ ] T [ ] T [ ] T [ ] T 9. d x dx dx For the differential equation 6 8x 0 with initial conditions x(0) = and dt dt dt t0 0, the solution is x(t) = e 6t e t x(t) = e t e 4t x(t) = e 6t e 4t x(t) = e t e 4t Page 5 of 3

6 GATE question papers: Electrical Engineering 00 (EE) Published by: 30. For the set of equations, x x x 3 4x 4 = and 3x 6x 3x x 4 = 6. The following statement is true Only the trivial solution x = x = x 3 = x 4 =0 exists There are no solutions A unique nontrivial solution exists Multiple nontrivial solutions exist 3. x (t) is a positive rectangular pulse from t = to t = with unit height as shown in the figure. The value of ( ) dω {where (ω) is the Fourier transform of x (t)} is x t 0 t 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 x n =, h n xn =,0,0,0, h[n] ={,0,0, } h[n] ={,0, } h[n] ={,,, } h[n] ={,, } 33. If the Ω resistor draws a current of A as shown in the figure, the value of resistance is A Ω A 4Ω 6Ω 8Ω 8Ω 34. The twoport network P shown in the figure has ports and, denoted by terminals (a, b) and (c, d), respectively. It has an impedance matrix with parameters denoted by z ij. A Ωresistor is connected in series with the network at port as shown in the figure. The impedance matrix of the modified twoport network (shown as a dashed box) is z z z z z z z z e Ω a b Ω p z z z z c d 6 z z z z Page 6 of 3

7 GATE question papers: Electrical Engineering 00 (EE) Published by: 35. The Maxwell's bridge shown in the figure is at balance. The parameters of the inductive coil are jωl 3 4 j / ωc = 3 / 4, L = C 4 3 L = 3 / 4, = C 4 3 = 4 / 3, L = (C 4 3 ) L = 4 / 3, = (C 4 3 ) 36. The frequency response of G(s) = / [s (s ) (s ) ] plotted in the complex G(j) plane (for o < < ) is Im ω = 0 Im 3/4 e ω = 0 ω = 0 Im 3/4 e ω = 0 /6 / The system x = Ax u with A =, = is 0 stable and controllable stable but uncontrollable unstable but controllable unstable and uncontrollable 38. The characteristic equation of a closedloop system is s(s)(s3)k(s)=0, k>0. Which of the following statements is true? Its roots are always real It cannot have a breakaway point in the range es < <0 Two of its roots tend to infinity along the asymptotes e[s] = It may have complex roots in the right half plane 39. A 50 Hz synchronous generator is i n i t i a l l y connected to a long lossless transmission line which is open circuited at the receiving end. With the f i e l d 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? Long Transmission Line e Im e receiving end 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 Page 7 of 3

8 GATE question papers: Electrical Engineering 00 (EE) Published by: 40. A separately excited dc machine is coupled to a 50Hz, threephase, 4pole induction machine as shown in the figure. The dc machine is energized first and the machines rotate at 600 rpm. Subsequently the induction machine is also connected to a 50 Hz, threephase source, the phase sequence being consistent with the direction of rotation. In steady state, DC Machine Induction machine 4pole,50Hz 50Hz, balanced three phase supply oth 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 oth machines act as motors 4. A balanced starconnected and purely resistive load is connected at the secondary of a stardelta transformer as shown in the figure. The linetoline voltage rating of the transformer is 0/0. Neglecting the nonidealities of the transformer, the impedance '' of the equivalent starconnected load, referred to the primary side of the transformer, is 0 /0 (3 j0) Ω (0.866 j0.5) Ω (0.866 j0.5) Ω ( j0) Ω 4. Consider a threephase, 50Hz, k 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 C 5C 5C e e r b y 4Ω 4Ω Conductor e = 3.74k, e =.6k e = 3.46k, e =.89k e = 6.0k, e = 4.3k e = 5.5k, e = 5.5k Page 8 of 3

9 GATE question papers: Electrical Engineering 00 (EE) Published by: 43. Consider a threecore, threephase, 50Hz, k cable whose conductors are denoted as, and in the figure. The interphase capacitance (C) between each pair of conductors is 0.F and the capacitance between each line conductor and the sheath is0.4 F. The perphase charging current is C C C Outer Sheath.0A.4A.7A 3.5A 44. For the power system shown in the figure below, the specifications of the components are the following: G: 5 k, 00 MA, =9% G: 5'k, 00MA, =9% T: 5 k/0 k, 90 MA, =% T: 0k/ 5 k, 90 MA, =% Line: 0 k, = 50 ohms G T C C Line us us Choose 5 k as the base voltage at the generator G, and 00 MA as the MA base. The impedance diagram is j0.8 G j0.8 G j0. G j0.7 j0.7 j0.7 j0.3 C j0.4 j0.7 j0.6 j0.7 j0.4 j0.7 j0.4 j0.3 T j0.8 G j0.8 G j0. G G j0. j0. G G Page 9 of 3

10 GATE question papers: Electrical Engineering 00 (EE) Published by: 45. The transistor circuit shown uses a s i l i c o n transistor with E = 0.7, I C I E and a dc current gain of 00. The value of 0 is 0 0kΩ 00Ω 50kΩ 4.65A The TTL circuit shown in the figure is fed with the waveform (also shown). All gates have equal propagation delay of 0 ns. The output of the circuit is 00 ns 0 t 0 t 0 t 0 0 t 0 t 47. When a "CALL Addr" instruction is executed, the CPU carries out the following sequential operations internally: Note: () means content of register (()) means content of memory location pointed to by PC means Program Counter SP means Stack Pointer (SP) incremented (PC) Addr (PC) Addr ((SP)) (PC) ((SP)) (PC) (SP) incremented (PC) Addr ((SP)) (PC) (SP) incremented ((SP)) (PC) (SP) incremented (PC) Addr Common Data Questions: 48 & 49 A separately excited DC motor runs at 500 rpm under noload with 00 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 400 rpm as shown in the figure. The rotational losses and armature reaction are neglected. speed rpm torque Nm Page 0 of 3

11 GATE question papers: Electrical Engineering 00 (EE) Published by: 48. The armature resistance of the motor is, Ω 3.4Ω 4.4Ω 7.7Ω 49. For the motor to deliver a torque of.5 Nm at 400 rpm the armature voltage to be applied is Common Data Questions: 50 & 5 Given f (t) and g (t) as shown below: f t 0 t g t g (t) can be expressed as t 3 t 3 g (t) = f (t 3) g (t) = f 3 g (t) = f t g (t) = f 5. The Laplace transform of g(t) is s s (e s 5 e ) s 5s 3 (e e s ) 3s e s ( e ) (e s 3 e ) s s Linked Answer Questions: Q.5 to Q.55 Carry Two Marks Each Statement for Linked Answer Questions: 5 & 53 The following Karnaugh map represents a function F. F A minimized from of the function F is F = F = F = s F = 53. Which of the following circuits is a realization of the above function F? F F F 0 t F Page of 3

12 GATE question papers: Electrical Engineering 00 (EE) Published by: Statement for Linked Answer Questions: 54 & 55 The LC circuit shown in the figure has an inductance L = mh and a capacitance C= 0F L t = 0 i C The initial current through the inductor is zero, while the initial capacitor voltage is 00. The switch is closed at t = 0. The current i through the circuit is: 5cos (5 0 3 t) A 5sin (0 4 t) A 0cos (5 0 3 t) A 0sin (0 4 t) A 55. The LC circuit of Q54 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 Q54. The switch is closed at t = 0. If the forward drop is negligible, the time taken for the device to turn off is L 00 t = 0 i 5A C 00 5s 56s 3s 6s Q. No Carry one Marks Each persons are in a room. 5 of them play hockey, 7 of them play football and 0 of them play both hockey and football. Then the number of persons playing neither hockey nor football is ) 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 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 59. Which of the following options is closest in meaning to the word: Circuitous? cyclic indirect confusing crooked 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 Q. No Carry Two Marks Each 6. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts: i. Hari s age Gita s age > Irfan s age Saira s age ii. The age difference between Gita and Saira is year. However Gita is not the oldest and Saira is not the youngest. iii. There are no twins. In what order were they born (oldest first)? HSIG SGHI IGSH IHSG 0Ω Page of 3

13 GATE question papers: Electrical Engineering 00 (EE) Published by: 6. 5 skilled workers can build a wall in 0days; 8 semiskilled workers can build a wall in 5 days; 0 unskilled workers can build a wall in 30days. If a team has skilled, 6 semiskilled and 5 unskilled workers, how long will it take to build the wall? 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. 64. Given digits,,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed? If 3776=435 how much is 7367? End of Question Paper Page 3 of 3

EE Branch GATE Paper 2010

EE Branch GATE Paper 2010 Q.1 Q.25 carry one mark each 1. The value of the quantity P, where, is equal to 0 1 e 1/e 2. Divergence of the three-dimensional radial vector field is 3 1/r 3. The period of the signal x(t) = 8 is 0.4