GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE

1. The cascode amplifier is a multistage configuration of 2. The circuit using a BJT with β = 50 and VBE = 0.7 V is shown in the figure. The base current IB and collector voltage V 3. For an npn transistor connected as shown in the figure, VBE = 0.7 volts. Given that reverse saturation current of the ju 4. Given $${r_d} = 20K\Omega ,\,\,{I_{DSS}}\, = \,10mA,\,\,{V_P} = - 8V$$ Zi and Zo of the circuit are respectively 5. Given $${r_d} = 20K\Omega ,\,\,{I_{DSS}}\, = \,10mA,\,\,{V_P} = - 8V$$ Transconductance in milli-Siemens (mS) and v 6. Given $${r_d} = 20K\Omega ,\,\,{I_{DSS}}\, = \,10mA,\,\,{V_P} = - 8V$$ ID and VDS under DC conditions are respectiv 7. For an n-channel MOSFET and its transfer curve shown in the figure, the threshold voltage is 8. The input resistance Ri of the amplifier shown in the figure is 9. The effect of current shunt feedback in an amplifier is to 10. In an ideal differential amplifier shown in the figure, a large value of (RE). 11. The voltage e0 indicated in the figure has been measured by an ideal voltmeter. Which of the following can be calculated 12. The Op-Amp circuit shown in figure is a filter. The type of filter and its cut-off frequency are respectively. 13. Given the ideal operational amplifier circuit shown in figure, indicate the correct transfer characteristics assuming id 14. Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth? 15. A device with input x(t) and output y(t) is characterized by: y(t) = x2(t). An FM signal with frequency deviation of 90 16. A carrier is phase modulated (PM) with frequency deviation of 10 kHz by a single tone frequency of 1 kHz. If the single 17. An output of a communication channel is a random variable 'V' with the probability density function as shown in the figu 18. Noise with uniform power spectral density of N0 W/Hz is passed through a filter H(ω ) = 2exp (-jωtd) followed by an ide 19. A signal as shown in figure is applied to a matched filter. Which of the following does represent the output of this mat 20. A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels 21. A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels 22. Despite the presence of negative feedback, control systems still have problems of instability because the 23. A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency ga 24. In the derivation of expression for peak percent overshoot,$$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\ti 25. A unity feedback system is given as,$$$G\left(s\right)=\frac{K\left(1-s\right)}{s\left(s+3\right)}$$$ indicate the corre 26. Which one of the following polar diagrams corresponds to a lag network? 27. The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \ri 28. The polar diagram of a conditionally stable system for open loop gain K=1 is shown in figure. The open loop transfer fun 29. The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \r 30. A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\ 31. A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X 32. Decimal 43 in Hexadecimal and BCD number system is respectively 33. The Boolean expression for the truth table shown is .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-famil 34. The Boolean function f implemented in the figure using two input multiplexers is 35. The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of counter is Q2 36. The present output Qn of an edge triggered JK flip-flop is logic 0. If J=1, then Qn+1 37. Both transistors T1 and T2 in figure have a threshold voltage of 1 Volt. The device parameters $${K_1}$$ and $${K_2}$$ o 38. The transistors used in a portion of the TTL gate shown in figure have β=100. the base-emitter voltage of is 0.7V for a 39. Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in Fig. represent 40. The magnetic field intensity vector of a plane wave is given by $$\overline H \left( {x,y,z,t 41. Characteristic impedance of a transmission line is 50$$\Omega $$. Input impedance of the open-circuited line is $${Z_{oc 42. Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $$\Omega $$ and a resisti 43. Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $$\Omega $$ and a resisti 44. Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of $${10^{14}}$$ Hz in glass. 45. Which one of the following does represent the electric field lines for the $$T{E_{02}}$$ mode in the cross-section of a 46. Two identical and parallel dipole antennas are kept apart by a distance $$\lambda /4$$ of in the H-plane. They are fed w 47. The primary reason for the widespread use of Silicon in semiconductor device technology is 48. A Silicon PN junction at a temperature of 20°C has a reverse saturation current of 10 pico-Amperes (pA). The reverse sat 49. The band gap of Silicon at room temperature is: 50. A silicon sample 'A' is doped with 1018 atoms/cm3 of Boron. Another sample 'B' of identical dimensions is doped with 101 51. The Zener diode in the regulator circuit shown in figure has a Zener voltage of 5.8 Volts and a Zener knee current of 0. 52. A Silicon PN junction diode under reverse bias has depletion region of width 10 µm. The relative permittivity of Silicon 53. A MOS capacitor made using p-type substrate is in the accumulation mode. The dominant charge in the channel is due to th 54. Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is 55. Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 56. If $$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matri 57. The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptst 58. $$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to 59. A fair dice is rolled twice. The probability that an odd number will follow an even number is 60. A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by 61. The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} + 62. Match the following and choose the correct combination Group $$-$$ $${\rm I}$$ $$E.$$ Newton $$-$$ Raphson method $$F.$$ 63. In what range should $$Re(s)$$ remain so that the laplace transform of the function $${e^{\left( {a + 2} \right)t + 5}}$ 64. The Dirac delta Function $$\delta \left( t \right)$$ is defined as 65. What memory address range is NOT represented by chip 1 and chip 2 in figure? A0 to A15 in this figure are the address li 66. Consider an 8085 microprocessor system The following program starts at locaton 0100H. LXI SP, 00FF LXI H, 0107 MVI 67. Consider an 8085 microprocessor system If in addition following code exists from 0109H onwards ORI 40H, ADD M What wi 68. Impedance Z as shown in the figure is: 69. The maximum power that can be transferred to the load resistor RL from the voltage source in figure is 70. For the circuit shown in figure, Thevenin’s voltage and Thevenin’s equivalent resistance at terminals a – b is 71. The condition on R, L and C such that the step response y(t) in figure has no oscillations, is 72. A square pulse of 3 volts amplitude is applied to C-R circuit shown in figure. The capacitor is initially uncharged. The 73. If R1 = R2 = R4 = R and R3 = 1.1R in the bridge circuit shown in figure, then the reading in the ideal voltmeter connect 74. In a series $$RLC$$ circuit $$R = 2\,k\Omega ,\,\,\,L = \,1H$$ and $$C = \,1/400\,\mu F.$$ The resonant frequency is 75. For the circuit in figure, the phase current $${{\rm I}_1}$$ is 76. The ABCD parameters of an ideal n:1 transformer shown in Fig. are $$\left[ {\matrix{ n & 0 \cr 0 & X \c 77. The h parameters of the circuit shown in Fig. are 78. Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined. 79. Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier tra 80. In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists? 81. A sequence x(n) has non-zero values as shown in Fig. The sequence $$$y(n)=\left\{\begin{array}{l}x\left(\frac n2-1\ri 82. A sequence x(n) has non-zero values as shown in figure. 1 The Fourier transform of y(2n) will be 83. The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} 84. Which of the following can be impulse response of a causal system? 85. The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5 x 86. For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by 87. A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency resp 88. The function x(t) is shown in Fig. Even and odd parts of a unit-step function u(t) are respectively. 89. The derivative of the symmetric function drawn in Fig .1 will look like 90. The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8} 91. Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is

$$\pi $$

2$$\pi $$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

Match the following and choose the correct combination.

GROUP 1
E- continuous and aperiodic signal
F- continuous and periodic signal
G- discrete and aperiodic signal
H- discrete and periodic signal

Group 2
1- Fourier representation is continuous and aperiodic
2- Fourier representation is discrete and aperiodic
3- Fourier representation is continuous and periodic
4- Fourier representation is discrete and periodic