GATE EE 2005 | GATE EE Year Wise Previous Years Questions

GATE EE

1. Assume that $${D_1}$$ and $${D_2}$$ in figure are ideal diodes the value of current $${I_s}$$ is 2. Assume that the $$N$$-channel $$MOSFET$$ shown in figure is ideal, and that its threshold voltage is The voltage $${\rm 3. The common emitter amplifier shown in the figure is biased using a $$1mA$$ ideal current source. The approximate base cu 4. Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characte 5. Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characte 6. Consider the inverting amplifier, using an ideal operational amplifier shown in figure. The designer wishes to realize t 7. In the given figure, if the input is a sinusoidal signal, the output-will appear as shown 8. The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in figure 9. When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error o 10. Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer functio 11. When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error 12. A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\l 13. The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( { 14. In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e 15. If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 r 16. A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & 17. A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & 18. In the figure, as long as $${X_1} = 1$$ and $${X_2} = 1,$$ the output $$Q$$ remains 19. The digital circuit shown in the figure works as a 20. Select the circuit which will produce the given output $$Q$$ for the input signals $${X_1}$$ and $${X_2}$$ given in the 21. If $${X_1}$$ and $${X_2}$$ are the inputs to the circuit shown in the figure, the output $$Q$$ is 22. A digital-to-analog converter with a full -scale output voltage of $$3.5$$ $$V$$ has a resolution close to $$14$$ $$m$$ 23. The $$8085$$ assembly language instruction that stores the content of $$H$$ and $$L$$ registers into the memory location 24. In the figure given below the value of $$R$$ is 25. In the given Fig. the Thevenin's equivalent pair (voltage, impedence), as seen at the terminals $$P-Q$$, is given by 26. In the Fig. given below, the initial capacitor voltage is zero. The switch is closed at $$t = 0.$$ the final steady-sta 27. A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has 28. The circuit shown in the Fig. is in steady state, when the switch is closed at $$t=0.$$ Assuming that the inductance is 29. A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has 30. The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{I 31. For the two port network shown in the Fig. the $$Z$$ $$-$$ matrix is given by 32. Two networks are connected in cascade as shown in the Fig. With the usual notations the equivalent $$A,B,C$$ and $$D$$ c 33. The set-up in the figure is used to measure resistance $$R$$. The ammeter and voltmeter resistances are $$0.01$$$$\Omega 34. A $$1000$$ $$V$$ $$DC$$ supply has two $$1-core$$ cables as its positive and negative leads: their insulation resistance 35. A DC ammeter has a resistance of $$0.1$$$$\Omega $$ and its current range is $$0$$ – $$100A.$$ If the range is to be ext 36. Two wattmeter's, which are connected to measure the total power on a three-phase system supplying a balanced load, read 37. A $$PMMC$$ voltmeter is connected across a series combination of a $$DC$$ voltage source $${V_1} = 2V$$ and $$AC$$ volta 38. The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an 39. A digital-to-analog converter with a full scale output voltage of $$3.5V$$ has resolution close to $$14mV.$$ It's bit si 40. Two magnetic poles revolve around a stationary armature carrying two coils ($$c_1-c'_1$$ , $$c_2-c'_2$$ ) as shown in Fi 41. In relation to DC machines, match the following and choose the correct combination. Group-I(Performance variables) (P) A 42. A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven (i) at half the rated sp 43. Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and 44. For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to: 45. On the torque/speed curve of induction motor shown in Fig, four points of operation are market as W, X, Y and Z. Which o 46. Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rate 47. A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting cu 48. Assertion [a]: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a w 49. In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve 50. In relation to the synchronous machines, which one of the following statements is false? 51. A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous 52. A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous 53. In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solutio 54. For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 55. If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } 56. For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to 57. If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value 58. for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1, 59. A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exac 60. If $$P$$ and $$Q$$ are two random events, then which of the following is true? 61. The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \r 62. For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \ri 63. The conduction loss versus device current characteristic of a power $$MOSFET$$ is best approximated by 64. The figure shows the voltage across a power semiconductor device and the current through the device during a switching t 65. An electronic switch $$S$$ is required to block voltages of either polarity during its OFF state as shown in figure (a). 66. A three - phase diode bridge rectifier is fed from a $$400$$ $$V$$ $$RMS$$. $$50$$ $$Hz$$, three $$-$$ phase $$AC$$ sour 67. Consider a phase $$-$$ controlled converter shown in figure The thyristor is fired at an angle $$\alpha $$ in every posi 68. The given figure shows a step $$-$$ down chopper switched at $$1$$ $$KHz$$ with a duty ratio $$D = 0.5.$$ The peak - pea 69. The output voltage waveform of a three - phase square-wave inverter contains 70. The insulation strength of an EHV transmission line is mainly governed by 71. At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power 72. A load centre is at an equidistant from the two thermal generating stations $${G_1}$$ and $${G_2}$$ as shown in figure. 73. A generator with constant 1.0 p.u. terminal voltage supplies power through a step-up transformer of 0.12 p.u. reactance 74. At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-li 75. The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and M 76. At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-li 77. The network shown in the given figure has impedances in p.u. as indicated. The diagonal element $$Y22$$ of the bus admit 78. High Voltage DC (HVDC) transmission is mainly used for 79. The p.u. parameters for a $$500$$ MVA machine on its own base are: Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. T 80. The RMS value of the voltage v(t) = 3 + 4cos(3t) is 81. The Fourier series for the function f(x) = sin2 x is 82. The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\inft 83. For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which 84. If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left( 85. For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to

GATE EE 2005

MCQ (Single Correct Answer)

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For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to GATE EE 2005 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 6 English