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.$$ The output characte 6. Consider the inverting amplifier, using an ideal operational amplifier shown in figure. The designer wishes to realize t 7. In the given figure, if the input is a sinusoidal signal, the output-will appear as shown 8. The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in figure 9. When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error o 10. Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer functio 11. When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error 12. The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( { 13. A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\l 14. In the $$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}$$ given in the 21. A digital-to-analog converter with a full -scale output voltage of $$3.5$$ $$V$$ has a resolution close to $$14$$ $$m$$ 22. If $${X_1}$$ and $${X_2}$$ are the inputs to the circuit shown in the figure, the output $$Q$$ is 23. The $$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$$ has 28. A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has 29. The circuit shown in the Fig. is in steady state, when the switch is closed at $$t=0.$$ Assuming that the inductance is 30. The $$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. 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 42. In relation to DC machines, match the following and choose the correct combination. Group-I(Performance variables) (P) A 43. Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and 44. 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 45. For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to: 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 $$(1, 59. If $$P$$ and $$Q$$ are two random events, then which of the following is true? 60. A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exac 61. The solution of the first order differential equation $$\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}$$ as shown in figure. 73. A generator with constant 1.0 p.u. terminal voltage supplies power through a step-up transformer of 0.12 p.u. reactance 74. The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and M 75. At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-li 76. At a $$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)

-0.6

If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left(z\right)=\frac1{z+1}$$ for k>0 is:

$$\left(-1\right)^k\delta\left(k\right)$$

$$\delta\left(k\right)-\left(-1\right)^k$$

$$\left(-1\right)^ku\left(k\right)$$

$$u\left(k\right)-\left(-1\right)^k$$

GATE EE 2005

MCQ (Single Correct Answer)

-0.6

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

GATE EE 2005 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 6 English

$$\sqrt {{1 \over 6}} $$

$$\sqrt {{1 \over 3}} $$

$${1 \over 3}$$

$$\sqrt {{2 \over 3}} $$

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2023