GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE

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

A sequence x(n) has non-zero values as shown in Fig. GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 11 English

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 11 English

The sequence $$$y(n)=\left\{\begin{array}{l}x\left(\frac n2-1\right)\;\;\;for\;n\;even\\0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;for\;n\;odd\end{array}\right.$$$
will be

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 11 English Option 1

GATE ECE 2005 Signals and Systems - Discrete Time Signal Fourier Series Fourier Transform Question 11 English Option 2

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined.

3sin(25t)

4cos(20t+3)+2sin(10t)

exp (−|t|) sin(25t)

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