GATE EE 2008 | GATE EE Year Wise Previous Years Questions

GATE EE

1. The truth of a monoshot shown in the figure is given in the table below: Two monoshots, one positive edge triggered and 2. A waveform generator circuit using $$OPAMPs$$ is shown in the figure. It produces a triangular wave at point $$'P'$$ wit 3. A general filter circuit is shown in figure The output of the filter in above is given to the circuit shown in figure 4. A general filter circuit is shown in figure If $${R_1} = {R_2} = {R_A}$$ and $${R_3} = {R_4} = {R_B},$$ the circuit ac 5. The block diagram of two types of half wave rectifiers are shown in figure. The transfer characteristics of the rectifie 6. Two perfectly matched silicon transistors are connected as shown in the figure. Assuming the $$\beta $$ of the transisto 7. In the voltage doubler circuit shown in figure, the switch $$' S '$$ is closed at $$t=0$$. Assuming diodes $${D_1}$$ &am 8. The equivalent circuits of a diode, during forward and reverse biased conditions are shown in figure. (a) (b) If suc 9. The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$ 10. The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is 11. The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is 12. The transfer function of two compensators are given below: $${C_1} = {{10\left( {s + 1} \right)} \over {\left( {s + 10} 13. The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure: This transfer function 14. Figure shows a feedback system where $$K>0$$ The range of $$k$$ for which system is stable will by given by 15. The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is 16. A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \rig 17. A $$3$$ line to $$8$$ line decoder, with active low outputs, is used to implement a $$3$$- variable Boolean function as 18. An input device is interfaced with Intel $$8085$$ $$A$$ microprocessor as memory mapped $${\rm I}/O,$$ the address of th 19. The contents (in Hexadecimal) of some of the memory locations in an $$8085A$$ based system are given below The content 20. The time constant for the given circuit will be 21. The number of chords in the graph of the given circuit will be 22. In the circuit shown in the figure, the value of the current $$i$$ will be given by 23. Assuming ideal elements in the circuit shown below, the voltage $${V_{ab}}$$ will be 24. The Thevenin's equivalent of a circuit operating at $$\omega = 5\,\,rad/s\,\,{V_{oc}} = 3.71\angle - {15.9^ \circ }$$ 25. Two $$8$$ $$A$$ $$D$$ $$C$$ $$s$$ one of single slope integrating type and other of successive approximation type. Take 26. Two Sinusoidal signal $$p\left( {{\omega _1}t} \right) = A\,\sin \omega t,$$ and $$q\left( {{\omega _2}t} \right)$$ are 27. The ac bridge shown in the figure is used to measure the impedance $$Z.$$ If the bridge is balanced for oscillator frequ 28. A bridge circuit is shown in the figure below. Which one of the sequence given below is most suitable for balancing the 29. A $$230V,$$ $$50Hz,$$ $$4$$ pole, single phase induction motor is rotating in the clockwise (forward) direction at a spe 30. A synchronous motor is connected to an infinite bus at $$1.0$$ $$p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power 31. A synchronous motor is connected to an infinite bus at $$1.0p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power facto 32. Distributed winding and short chording employed in AC machines will result in 33. In a stepper motor, the detent torque means 34. A $$3$$-phase, $$440$$ $$V,$$ $$50$$ $$Hz,$$ $$4$$ pole, slip ring induction motor is feed from the rotor side through 35. A $$3$$-phase, $$440$$ $$V,$$ $$50$$ $$Hz,$$ $$4$$ pole, slip ring induction motor is feed from the rotor side through 36. A $$400$$ $$V,$$ $$50$$ $$Hz,$$ $$30$$ $$hp,$$ three-phase induction motor is drawing $$50$$ A current at $$0.8$$ power 37. A $$400$$ $$V,$$ $$50$$ $$Hz$$, $$4$$ pole, $$1400$$ $$rpm$$, star connected squirrel cage induction motor has the foll 38. The core of two-winding transformer is subjected to a magnetic flux variation as indicated in the figure. The induce 39. Three single-phase transformers are connected to form a $$3$$-phase transformer bank. The transformers are connected in 40. It is desired to measure parameters of $$230$$ $$V/115$$ $$V,$$ $$2$$ $$kVA$$, single-phase transformers. The following 41. A $$240V$$ $$dc$$ shunt motor draws $$15A$$ while supplying the rated load at a speed of $$80$$ $$rad/s$$. The armatur 42. A $$240V$$ $$dc$$ shunt motor draws $$15A$$ while supplying the rated load at a speed of $$80$$ $$rad/s$$. The armatur 43. A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space betw 44. Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( 45. A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of 46. Equation $${e^x} - 1 = 0\,\,$$ is required to be solved using Newton's method with an initial guess $$\,\,{x_0} = - 1.\ 47. Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ 48. A differential equation $${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$ has to be solved using trapezoidal 49. $$X$$ is uniformly distributed random variable that take values between $$0$$ and $$1.$$ The value of $$E\left( {{X^3}} 50. Let $$P$$ be $$2x2$$ real orthogonal matrix and $$\overline x $$ is a real vector $${\left[ {\matrix{ {{x_1}} & { 51. $$A$$ is $$m$$ $$x$$ $$n$$ full rank matrix with $$m > n$$ and $${\rm I}$$ is an identity matrix. Let matrix $${A^ + 52. If the rank of a $$5x6$$ matrix $$Q$$ is $$4$$ then which one of the following statements is correct? 53. The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as $$\alpha \left( \lambda \right) = \ 54. In the single phase voltage controller circuit shown in the figure, for what range of triggering angle $$\left( \alpha 55. A single phase fully controlled converter bridge is used for electrical braking of a separately excited $$dc$$ motor. Th 56. A single - phase half controlled converter shown in the figure feeding power to highly inductive load. The converter is 57. A single phase voltage source inverter is feeding a purely inductive load as shown in the figure. The inverter is oper 58. A $$3$$ - phase voltage source Inverter is operated in $${180^ \circ }$$ conduction mode. Which one of the following sta 59. In the circuit shown in the figure, the switch is operated at a duty cycle of $$0.5.$$ A large capacitor current is conn 60. A single phase full bridge converter supplies a load drawing constant and ripple free load current. If the triggering an 61. A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $$1 62. A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the syste 63. Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0. 64. Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0. 65. Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0. 66. A 3-phase transmission line is shown in figure: Voltage drop across the transmission line is given by the following eq 67. A lossless single machine infinite bus power system is shown below: The synchronous generator transfers $$1.0$$ per un 68. A lossless transmission line having Surge Impedance Loading $$(SIL)$$ of $$2280$$ $$MW.$$ A Series capacitive compensa 69. An extra high voltage transmission line of length $$300$$ km can be approximate by a lossless line having propagation co 70. A two machine power system in shown below. Transmission line $$XY$$ has positive sequence impedance of $${Z_1}\Omega $$ 71. Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit bu 72. A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Give 73. The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ 74. A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha $$ is a real constant $$\left( {\sin \,c 75. A system with input $$x(t)$$ and output $$y(t)$$ is defined by the input $$-$$ output relation: $$y\left( t \right) = \ 76. The impulse response of a causal linear time-invariant system is given as $$h(t)$$. Now consider the following two state 77. A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Give 78. Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)zn-1 at z = a for n $$\geq 79. A function y(t) satisfies the following differential equation:$$$\frac{\operatorname dy\left(t\right)}{\operatorname dt} 80. Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t0) + x(t + t0) for some t0. The Fourier Series coeff

GATE EE 2008

MCQ (Single Correct Answer)

-0.6

A function y(t) satisfies the following differential equation:$$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\left(t\right)$$$ where $$\delta\left(t\right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form

e^t

e^-t

e^tu(t)

e^-tu(t)

GATE EE 2008

MCQ (Single Correct Answer)

-0.6

Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t₀) + x(t + t₀) for some t₀. The Fourier Series coefficient of y(t) are denoted by b_k. If b_k=0 for all odd k, then t₀ can be equal to

T/8

T/4

T/2

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