GATE EE 2005 | GATE EE Year Wise Previous Years Questions

GATE EE

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

GATE EE 2005

MCQ (Single Correct Answer)

-0.6

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 of the following values as t$$\rightarrow\infty$$ ?