GATE EE 2004 | GATE EE Year Wise Previous Years Questions

GATE EE

1. The current through the zener diode in the given circuit is 2. Assuming that the diodes are ideal in figure the current in the diode $${D_1}$$ is 3. Two perfectly matched silicon transistors are connected as shown in figure. The value of the current $${\rm I}$$ is 4. A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cutoff region (OFF state) or 5. The value of $$R$$ for which the $$PMOS$$ transistor in Figure. $$Q$$ $$63$$ will be biased in linear region is 6. In the Schmitt trigger circuit shown in figure, if $${V_{CE}}\left( {sat} \right) = 0.1V,$$ the output logic low level $ 7. The input resistance $${R_{IN}}\left( { = {V_x}/{I_x}} \right)$$ of the circuit in the figure is 8. In the active filter circuit shown in figure, if $$Q=1,$$ a pair of poles will be realized with $${\omega _0}$$ equal to 9. The transconductance $${g_m}$$ of the transistor shown in figure is $$10$$ $$mS.$$ The value of input resistance $${R_{i 10. For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the outpu 11. For the block diagram shown in figure, the transfer function $${{C\left( s \right)} \over {R\left( s \right)}}$$ is equa 12. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 13. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 14. Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace 15. The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12. 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. For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be 18. A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( { 19. The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1, 20. The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s 21. In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will 22. The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ 23. The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline 24. 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 25. The digital circuit using two inverters shown in figure will act as 26. The digital circuit shown in figure generates a modified clock pulse at the output. Choose the correct output waveform f 27. The voltage comparator shown in Fig. can be used in the analog-to-digital conversion as 28. In Fig., the value of the source voltage is 29. In Fig., $${R_a},\,\,{R_b},$$ and $${R_c}$$ are $$20\,\Omega ,\,\,10\,\Omega $$ and $$10\,\Omega $$ respectively. The re 30. In Fig., the value of resistance $$R$$ in $$\Omega $$ is 31. In figure, the capacitor initially has a charge of $$10$$ Coulomb. The current in the circuit one second after the switc 32. The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is 33. In Fig. the admittance values of the elements in Siemens are $${Y_R} = 0.5 + j0,$$ $${Y_L} = 0 - j\,1.5,$$ $${Y_C} = 34. The $$Z$$ matrix of a $$2$$ $$-$$ port network is given by $$\left[ {\matrix{ {0.9} & {0.2} \cr {0.2} & 35. A galvanometer with a full scale current of $$10$$ $$mA$$ has a resistance of $$1000$$$$\Omega $$. The multiplying power 36. A moving coil of a meter has $$100$$ turns, and a length and depth of $$10$$ $$mm$$ and $$20$$ $$mm$$ respectively. It i 37. A moving iron ammeter produces a full scale torque of $$240$$ $$\,\mu Nm$$ with a deflection of $${120^ \circ }$$ at a c 38. The circuit in fig is used to measure the power consumed by the load. The current coil and the voltage coil of the watt 39. A single-phase load is connected between $$R$$ and $$Y$$ terminals of a $$415$$ $$V,$$ symmetrical, $$3$$-phase, $$4$$-w 40. 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 41. A $$50$$ $$Hz,$$ bar primary $$CT$$ has a secondary with $$500$$ turns. The secondary supplies $$5A$$ current into a pur 42. The core flux in the $$CT$$ of above problem under the given operating condition is 43. A $$CRO$$ probe has an impedance of $$500k\Omega $$ in parallel with a capacitance of $$10pF$$. The probe is used to mea 44. 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 45. 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 46. The resistance and reactance of a 100 kVA 11000|400 V, $$\triangle$$ - Y distribution transformer are 0.02 and 0.07 pu r 47. 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 48. A 50 kVA, 3300/230 V single-phase transformers is connected as an autotransformer shown in figure. The nominal rating of 49. The type of single-phase induction motor having the highest power factor at full load is 50. The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage 51. For a linear electromagnetic circuit, the following statement is true. 52. A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand still impedances Main wind 53. A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of the 54. 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 55. For a given stepper motor, the following torque has the highest numerical value. 56. The following motor definitely has a permanent magnet rotor 57. The synchronous speed for the seventh space harmonic $$mmf$$ wave of a $$3$$-phase, $$8$$ pole, $$50$$ $$Hz$$ induction 58. Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per ph 59. A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchro 60. For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed 61. A $$500$$ $$MW$$ $$3$$-phase $$Y$$-connected synchronous generator has a rated voltage of $$21.5kV$$ at $$0.85$$ $$pf.$$ 62. A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce p 63. A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$m 64. The inductance of a long solenoid of length $$1000$$ $$mm$$ wound uniformly with $$3000$$ turns on a cylindrical paper t 65. The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______. 66. A bipolar junction transistor $$(BJT)$$ is used as a power control switch by biasing it in the cut-off region (OFF state 67. The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of $$10$$ $$mA,$$ for gu 68. A $$MOSFET$$ rated for $$15 A,$$ carries a periodic current as shown in figure. The ON state resistance of the MOSFET is 69. The circuit in figure shows a full-wave rectifier. The input voltage is $$230$$ $$V$$ $$(rms)$$ single-phase ac. The pea 70. The circuit in figure shows a $$3$$ $$-$$ phase half $$-$$ wave rectifier. The source is a symmetrical, $$3$$ $$-$$ phas 71. Figure shows a chopper. The device $${S_1}$$ is the main switching device. $${S_2}$$ is the auxiliary commutation device 72. Figure shows a chopper operating from a $$100$$ $$V$$ $$dc$$ input. The duty ratio of the main switch $$S$$ is $$0.8.$$ 73. The triac circuit shown in figure controls the $$ac$$ output power to the resistive load. The peak power dissipation in 74. Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is 75. The rated voltage of a $$3$$-phase power system is given as 76. The phase sequence of the $$3$$-phase system shown in figure is 77. The generalized circuit constants of a $$3$$-phase, $$220$$ $$kV$$ rated voltage, medium length transmission line are $$ 78. A lightning stroke discharges impulse current of $$10$$ kA (peak) on a $$400$$ kV transmission line having surge impedan 79. A $$800$$ $$kV$$ transmission line is having per phase line inductance of $$1.1$$ $$mH/km$$ and per phase line capacitan 80. A $$110$$ $$kV,$$ single core coaxial, XLPE insulated power cable delivering power at $$50$$ $$Hz,$$ has a capacitance o 81. A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fau 82. A 3-phase transmission line supplies $$\Delta - $$ connected load Z. The conductor $$'c'$$ of the line develops an open 83. A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly g 84. A $$3$$-phase generator rated at $$110$$ MVA, $$11$$ kV is connected through circuit breakers to a transformer. The g 85. The transmission line distance protection relay having the property of being inherently directional is 86. In thermal power plants, the pressure in the working fluid cycle is developed by 87. For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adju 88. A new generator having $${E_g} = 1.4\,\angle {30^ \circ }\,$$ pu [ equivalent to ($$1.212 +j$$ $$0.70$$)pu ] and synchro 89. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current 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 periodic waveform given in Fig. is

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GATE EE 2004

MCQ (Single Correct Answer)

-0.6

For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be

zero

one

two

three

GATE EE 2004

MCQ (Single Correct Answer)

-0.6

A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {1 - s} \right)} \over {\left( {1 + s} \right)}}$$

$$\left| K \right| > 1$$

$$K > 1$$

$$\left| K \right| < 1$$

$$K < - 1$$

GATE EE 2004

MCQ (Single Correct Answer)

-0.3

The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,j0)$$ in the $$G(s) H(s)$$ plane. The phase margin of the system is

$${0^0}$$

$${45^0}$$

$${90^0}$$

$${180^0}$$

GATE EE 2004

MCQ (Single Correct Answer)

-0.6

The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of $$‘a’$$ to give a phase margin of $${45^0}$$ is equal to

$$0.141$$

$$0.441$$

$$0.841$$

$$1.141$$

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2024