GATE EE 2004 | GATE EE Year Wise Previous Years Questions

GATE EE

1. In the active filter circuit shown in figure, if $$Q=1,$$ a pair of poles will be realized with $${\omega _0}$$ equal to 2. The input resistance $${R_{IN}}\left( { = {V_x}/{I_x}} \right)$$ of the circuit in the figure is 3. In the Schmitt trigger circuit shown in figure, if $${V_{CE}}\left( {sat} \right) = 0.1V,$$ the output logic low level $ 4. The transconductance $${g_m}$$ of the transistor shown in figure is $$10$$ $$mS.$$ The value of input resistance $${R_{i 5. The value of $$R$$ for which the $$PMOS$$ transistor in Figure. $$Q$$ $$63$$ will be biased in linear region is 6. A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cutoff region (OFF state) or 7. Two perfectly matched silicon transistors are connected as shown in figure. The value of the current $${\rm I}$$ is 8. Assuming that the diodes are ideal in figure the current in the diode $${D_1}$$ is 9. The current through the zener diode in the given circuit is 10. The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ 11. In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will 12. The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s 13. The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1, 14. A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( { 15. For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be 16. The block diagram of a closed loop control system is given by figure. The values of $$K$$ and $$P$$ such that the system 17. The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12. 18. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 19. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 20. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 21. For the block diagram shown in figure, the transfer function $${{C\left( s \right)} \over {R\left( s \right)}}$$ is equa 22. For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the outpu 23. The voltage comparator shown in Fig. can be used in the analog-to-digital conversion as 24. The digital circuit shown in figure generates a modified clock pulse at the output. Choose the correct output waveform f 25. The digital circuit using two inverters shown in figure will act as 26. A digital circuit which compares two numbers $${A_3}{A_2}{A_1}{A_0},\,\,{B_3}{B_2}{B_1}{B_0}$$ is shown in Fig. To get o 27. The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline 28. In Fig., the value of the source voltage is 29. The $$Z$$ matrix of a $$2$$ $$-$$ port network is given by $$\left[ {\matrix{ {0.9} & {0.2} \cr {0.2} & 30. In Fig. the admittance values of the elements in Siemens are $${Y_R} = 0.5 + j0,$$ $${Y_L} = 0 - j\,1.5,$$ $${Y_C} = 31. The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is 32. In figure, the capacitor initially has a charge of $$10$$ Coulomb. The current in the circuit one second after the switc 33. In Fig., the value of resistance $$R$$ in $$\Omega $$ is 34. In Fig., $${R_a},\,\,{R_b},$$ and $${R_c}$$ are $$20\,\Omega ,\,\,10\,\Omega $$ and $$10\,\Omega $$ respectively. The re 35. A single-phase load is connected between $$R$$ and $$Y$$ terminals of a $$415$$ $$V,$$ symmetrical, $$3$$-phase, $$4$$-w 36. A $$CRO$$ probe has an impedance of $$500k\Omega $$ in parallel with a capacitance of $$10pF$$. The probe is used to mea 37. The core flux in the $$CT$$ of above problem under the given operating condition is 38. A $$50$$ $$Hz,$$ bar primary $$CT$$ has a secondary with $$500$$ turns. The secondary supplies $$5A$$ current into a pur 39. A dc A-h meter is rated for 15 A, 250V. The meter constant is 14.4 A-sec/rev. The meter constant at rated voltage may be 40. The circuit in fig is used to measure the power consumed by the load. The current coil and the voltage coil of the watt 41. A moving iron ammeter produces a full scale torque of $$240$$ $$\,\mu Nm$$ with a deflection of $${120^ \circ }$$ at a c 42. A moving coil of a meter has $$100$$ turns, and a length and depth of $$10$$ $$mm$$ and $$20$$ $$mm$$ respectively. It i 43. A galvanometer with a full scale current of $$10$$ $$mA$$ has a resistance of $$1000$$$$\Omega $$. The multiplying power 44. The synchronous speed for the seventh space harmonic $$mmf$$ wave of a $$3$$-phase, $$8$$ pole, $$50$$ $$Hz$$ induction 45. A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce p 46. A $$500$$ $$MW$$ $$3$$-phase $$Y$$-connected synchronous generator has a rated voltage of $$21.5kV$$ at $$0.85$$ $$pf.$$ 47. For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed 48. A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchro 49. Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per ph 50. A 400 V, 15 kW, 4 pole, 50 Hz, Y-connected induction motor has full load slip of 4%. The output torque of the machine at 51. The following motor definitely has a permanent magnet rotor 52. For a given stepper motor, the following torque has the highest numerical value. 53. A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of the 54. A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand still impedances Main wind 55. For a linear electromagnetic circuit, the following statement is true. 56. The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage 57. The type of single-phase induction motor having the highest power factor at full load is 58. A 50 kVA, 3300/230 V single-phase transformers is connected as an autotransformer shown in figure. The nominal rating of 59. A 500 kVA, 3-phase transformer has iron loses of 300 W and full load copper losses of 600 W. The percentage load at whic 60. The resistance and reactance of a 100 kVA 11000|400 V, $$\triangle$$ - Y distribution transformer are 0.02 and 0.07 pu r 61. A 8 pole, DC generator has a simplex wave-wound armature containing 32 coils of 6 turns each. Its flux per pole is 0.06 62. The armature resistance of a permanent magnet dc motor is 0.8 $$\Omega$$. At no load, the motor draws 1.5 A from a suppl 63. The inductance of a long solenoid of length $$1000$$ $$mm$$ wound uniformly with $$3000$$ turns on a cylindrical paper t 64. A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$m 65. The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______. 66. The triac circuit shown in figure controls the $$ac$$ output power to the resistive load. The peak power dissipation in 67. Figure shows a chopper operating from a $$100$$ $$V$$ $$dc$$ input. The duty ratio of the main switch $$S$$ is $$0.8.$$ 68. Figure shows a chopper. The device $${S_1}$$ is the main switching device. $${S_2}$$ is the auxiliary commutation device 69. The circuit in figure shows a $$3$$ $$-$$ phase half $$-$$ wave rectifier. The source is a symmetrical, $$3$$ $$-$$ phas 70. The circuit in figure shows a full-wave rectifier. The input voltage is $$230$$ $$V$$ $$(rms)$$ single-phase ac. The pea 71. A $$MOSFET$$ rated for $$15 A,$$ carries a periodic current as shown in figure. The ON state resistance of the MOSFET is 72. The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of $$10$$ $$mA,$$ for gu 73. A bipolar junction transistor $$(BJT)$$ is used as a power control switch by biasing it in the cut-off region (OFF state 74. A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fau 75. A $$110$$ $$kV,$$ single core coaxial, XLPE insulated power cable delivering power at $$50$$ $$Hz,$$ has a capacitance o 76. A $$800$$ $$kV$$ transmission line is having per phase line inductance of $$1.1$$ $$mH/km$$ and per phase line capacitan 77. A lightning stroke discharges impulse current of $$10$$ kA (peak) on a $$400$$ kV transmission line having surge impedan 78. The generalized circuit constants of a $$3$$-phase, $$220$$ $$kV$$ rated voltage, medium length transmission line are $$ 79. The phase sequence of the $$3$$-phase system shown in figure is 80. The rated voltage of a $$3$$-phase power system is given as 81. Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is 82. A 3-phase transmission line supplies $$\Delta - $$ connected load Z. The conductor $$'c'$$ of the line develops an open 83. A new generator having $${E_g} = 1.4\,\angle {30^ \circ }\,$$ pu [ equivalent to ($$1.212 +j$$ $$0.70$$)pu ] and synchro 84. For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adju 85. In thermal power plants, the pressure in the working fluid cycle is developed by 86. The transmission line distance protection relay having the property of being inherently directional is 87. A $$3$$-phase generator rated at $$110$$ MVA, $$11$$ kV is connected through circuit breakers to a transformer. The g 88. A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly g 89. The $$rms$$ value of the periodic waveform given in Fig. is 90. In the system shown in Fig. the input $$x\left( t \right) = \sin t.$$ In the steady-state, the response $$y(t)$$ will be 91. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current

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GATE EE 2004

MCQ (Single Correct Answer)

-0.6

The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \ge 0.$$
The steady-state value of the unit step response of the system is equal to

$$0$$

$$0.25$$

$$0.5$$

$$1.0$$

GATE EE 2004

MCQ (Single Correct Answer)

-0.3

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to

$$5$$

$$5/2$$

$$5/3$$

$$0$$

GATE EE 2004

MCQ (Single Correct Answer)

-0.3

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to

$$5$$

$$5/2$$

$$5/3$$

$$0$$

GATE EE 2004

MCQ (Single Correct Answer)

-0.3

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$f(t)$$ is equal to

$$5$$

$$5/2$$

$$5/3$$

$$0$$

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2024