GATE ECE 2008 | GATE ECE Year Wise Previous Years Questions

GATE ECE

1. In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta $$ and all the capacitances are very large. T 2. Consider the Schmitt trigger circuit shown below. A triangular wave which goes from -12V to 12V is applied to the inve 3. The Op-Amp circuit shown above represents a 4. Consider the following circuit using an ideal Op-Amp. The I-V characteristics of the diode is described by the relation 5. In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta $$ and all the capacitances are very large. 6. Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a se 7. A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n 8. A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each 9. A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea 10. A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea 11. Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM 12. Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-d 13. The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is 14. Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating th 15. A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. 16. Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step re 17. The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$ 18. A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s 19. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the f 20. A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is 21. Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition $ 22. The pole-zero plot given below corresponds to a 23. The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes t 24. The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over { 25. The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes t 26. In the following circuit, the comparator output is logic “I” if V1 > V2 and is logic “0” otherwise. The D/A conversio 27. In the following circuit, the comparator output is logic “I” if V1 > V2 and is logic “0” otherwise. The D/A conversio 28. The logic function implemented by the following circuit at the terminal OUT is 29. For each of the positive edge-triggered J-K flip flop used in the following future, the propagation delay is $$\Delta $$ 30. Which of the follwing Boolean expression correctly represents the relation between P, Q, R and M1? 31. For the circuit shown in the following figure $${I_0}$$ - $${I_3}$$ are inputs to the 4:1 multiplexer R(MSB) and S are c 32. One end of loss-less transmission line having the characteristic impedance of 75 $$\Omega $$ and length of 1 cm is short 33. At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is 34. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is 35. A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The min 36. A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant 37. The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ a 38. Which of the following is true? 39. The drain current of a MOSFET in saturation is given by $$I_D\;=\;K\left(V_{GS}\;-V_T\right)^2$$ where 'K' is a constant 40. A silicon wafer has 100 mm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidati 41. Which of the following is NOT associated with a P-N junction? 42. In the following limiter circuit, an input voltage $${\mathrm V}_\mathrm i\;=\;10\sin\left(100\mathrm{πt}\right)$$ appli 43. Two identical NMOS transistors M1 and M2 are connected as shown below. Vbias is chosen so that both transistors are in s 44. The measured transconductance gm of an NMOS transistor operating in the linear region is plotted against the gate voltag 45. For the circuit shown in the following figure, transistors M1 and M2 are identical NMOS transistors. Assume that M2 is i 46. The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has 47. The residue of the function $$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is 48. The equation sin(z) = 10 has 49. The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is 50. Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right) 51. Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q 52. In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \p 53. Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0 54. The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line 55. For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is 56. All the four entries of $$2$$ $$x$$ $$2$$ matrix $$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21 57. An 8085 executes the following instructions 2710 LXI H, 30A0H DAD H PCHL All addresses and constants are in Hex. L 58. The driving point impedance of the following network is given by $$Z(s) = {{0.2\,s} \over {{s^2}\, + \,0.1\,s\, + \,2}}$ 59. A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme 60. A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme 61. In the following graph, the number of trees (P) and the number of cut-sets (Q) are 62. The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The 63. The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For 64. The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For 65. In the following circuit, the switch S is closed at t=0. The rate of change of current $$\frac{di}{dt}(0^+)$$ is given b 66. The Thevenin equivalent impedance Zth between the nodes P and Q in the following circuit is 67. Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with 68. A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ 69. The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr 70. A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 an 71. The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptio 72. The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\e 73. In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency 74. In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequ 75. {x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT)

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
y (n) = $${1 \over N}\,\sum\limits_{r = 0}^{N - 1} x \,\left( r \right)x\,(n + r\,)$$ is