GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE

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

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

In what range should Re(s) remain so that the Laplace transform of the function e^(a+2)t+5 exists?

Re(s) > a+2

Re(s) > a+7

Re(s) < 2

Re(s) > a+5

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier transform of y(n). Then Y ($$({e^{jo}})$$ is