ECE Branch GATE Paper (C) exp ( t ) sin (25t) (B) 4cos (20t + 3) + 2 sin (710t)

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1 Question 30 Carry One Mark Each. The following differential equation has 2 3 d y dy y 2 2 dt degree = 2, order = degree = 3, order = = x dt degree = 4, order = 3 degree = 2, order = 3 2. Choose the function ; < t <, for which a Fourier series cannot be defined. 3 sin (25t) exp ( t ) sin (25t) 4cos (20t + 3) + 2 sin (70t) 3. A fair dice is rolled twice. The probability that an odd number will follow an even number is A solution of the following differential equation is given by 2 d y dy 5 6y 0 2 dx dx + = 2x 3x y = e + e x y = e + e 2x 3x x y = e + e y = e + e 2 3x 2 3x 5. The function is shown in the figure. Even and odd parts of a unit step function are respectively, 0 t Page :

2 6. The region of convergence of Z transform of the sequence must be z < z > 7. The condition on R, L and C such that the step response in the figure has no oscillations, is L R C 8. The ABCD parameters of an ideal n: transformer shown in the figure are. The value of X will be n: n Page : 2

3 9. In a series RLC circuit, R = 2 kω, L = H, and The resonant frequency is 0. The maximum power that can be transferred to the load resistor from the voltage source in the figure is 000Ω 0V R L W 0W. The bandgap of silicon at room temperature is.3 ev 0.7 ev 0.25W 0.5W. ev.4 ev 2. A silicon PN junction at a temperature of C has a reverse saturation current of 0 pico- Amperes (pa). The reverse saturation current at C for the same bias is approximately 30 pa. 40 pa. 50pA. 60pA 3. The primary reason for the widespread use of Silicon in semiconductor device technology is aboundance of Silicon on the surface of the Earth. larger bandgap of Silicon in comparison to Germanium. favorable properties of Silicon dioxide ( ). lower melting point. 4. The effect of current shunt feedback in an amplifier to increase the input resistance and decrease the output resistance. increase both input and output resistances. decrease both input and output resistances. decrease the input resistance and increase the output resistance. Page : 3

4 5. The input resistance of the amplifier shown in the figure is 30k 0k + ~ Ideal operational amplifier Infinite 6. The first and the last critical frequency of an RC driving point impedance function must respectively be a zero and a pole a pole and a pole a zero and a zero a pole and a zero 7. The cascode amplifier is a multistage configuration of CC CB CE CB CB CC CE CC 8. Decimal 43 in Hexadecimal and BCD number system is respectively B2, B, B, B2, The Boolean function implemented in the figure using two input multiplexers is C 0 0 A B E Page : 4

5 20. Which of the following can be impulse response of a casual system? h(t) h(t) t t h(t) h(t) t t Page : 5

6 2. Let be the Fourier transform of Then is Find the correct match between group and group 2. Group I P - {+ km (t)} A Q A ) R - A S A Group II W - Phase modulation X - Frequency modulation Y Amplitude modulation Z - DSB-SC modulation P Z, Q Y, R X, S W, P W, Q X, R Y, S Z, 23. The power in the signal is 40 4 P X, Q W, R Z, S Y, P Y, Q Z, R W, S X, Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth? VSB SSB DSB-SC AM 25. A linear system is equivalently represented by two sets of state equations. The eigenvalues of the representations are also computed as Which one of the following statements is true? and Page : 6

7 26. Which one of the following polar diagrams corresponds to a lag network? I m = 0 = I m Re = 0 = Re I m = = 0 Re Page : 7

8 I m = = 0 Re 27. Despite the presence of negative feedback, control systems still have problems of instability because the components used have nonlinearities. dynamic equations of the subsystems are not known exactly. mathematical analysis involves approximations. system has large negative phase angle at high frequencies. 28. The magnetic field intensity vector of a plane wave is given by, Where denotes the unit vector in direction. The wave is propagating with a phase velocity 29. Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure represent Unit circles. Constant resistance circles. Page : 8

9 Constant reactance circles. Constant reflection coefficient circles. 30. Refractive index of glass is.5. Find the wavelength of a beam of light with a frequency of Hz in glass. Assume velocity of light is 3 m/s in vacuum. 3 3 mm 2 Question 3 80 Carry Two Marks Each 3. In what range should Re(s) remain so that the Laplace transform of the function exits? Re(s) > a + 2 Re(s) > a + 7 Re(s) < 2 Re(s) > a Given the matrix, the eigenvector is 33. Let, A= and = Then (a + b)= 34. The value of the integral π 2 x I = exp dx 2π 8 0 is 2 2π 35. The derivative of the symmetric function drawn in given figure will look like Page : 9

10 36. Match the following and choose the correct combination : Group Group 2 E. Newton Raphson method. Solving nonlinear equations F. Runge kutta method 2. Solving linear simultaneous equations G. Simpson s Rule 3. Solving ordinary differential equations H. Gauss elimination 4. Numerical integration method 5. Interpolation 6. Calculation of Eigenvalues E 6, F, G 5, H 3 E, F 6, G 4, H 3 E, F 3, G 4, H 2 E 5, F 3, G 4, H Page : 0

11 37. Given an orthogonal matrix A = is 38. For the circuit show in the figure, the instantaneous current is j2ω j2ω 5 0 A 3Ω 0 60 A 39. Impedance Z as shown in the given figure is j2ω j5ω j0ω j0ω j2ω Z Page :

12 40. For the circuit shown in the figure, Thevenin s voltage and Thevenin s equivalent resistance atterminals is 5Ω 5Ω a b 0V 4. If and in the bridge circuit shown in the figure, then the reading in the ideal voltmeter connected between and is 0V a V b V V V. V. 42. The parameters of the circuit shown in the figure are 0Ω Ω Page : 2

13 43. A square pulse of 3 volts amplitude is applied to C R circuit shown in the figure. The capacitor is initially uncharged. The output voltage at time is 3V + 0.μF -j2ω kω 3V -3V 2sec 4V -4V 44. A Silicon sample A is doped with of Boron. Another sample B of identical dimensions is doped with of Phosphorus. The ratio of electron to hole mobility is 3. The ratio of conductivity of the sample A to B is A Silicon PN junction diode under reverse bias has depletion region of width. The relative permittivity of Silicon, and the permittiveity of free space The depletion capacitance of the diode per square meter is t For an npn transistor connected as shown in the figure, = 0.7 volts. Given that reverse saturation current of the junction at room temperature K is A, the emitter current is Page : 3

14 30 ma. 39 ma. 49 ma. 20 ma. 47. The voltage indicated in the figure has been measured by an ideal voltmeter. Which of the following can be calculated? M M Bias current of the inverting input only Bias current of the inverting and non inverting inputs only Input offset current only Both the bias currents and the input offset current. Page : 4

15 48. The OP amp circuit shown in the figure is a filter. The type of filter and its cut off frequency are respectively 0K 0K µf K High pass, 000 rad / sec. Low pass, 000 rad / sec. High pass, 0000 rad / sec. Low pass, 0000 rad / sec. 49. In an ideal differential amplifier shown in the figure, a large value of ( ). Increases both the differential and common Increases the common mode gain only. Decreases the differential mode gain only. Decreases the common mode gain only. mode gains. Page : 5

16 50. For an n channel MOSFET and its transfer curve shown in the figure, the threshold voltage is = 5V D Transfer characteristics G = 3V V S = V V and the device is in active region. V and the device is in saturation region. V and the device is in saturation region. V and device is in active region. 5. The circuit using a BJT with and is shown in the figure. The base current and collector voltage are respectively 430Ω 2kΩ 20V 0µF V 0 kω 40µF Page : 6

17 52. The zener diode in the regulator circuit show in the figure has a Zener voltage of 5.8 volts and a Zener knee current of 0.5 ma. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 volts, is = 5.8 Load 23.7 ma. 4.2 ma. 3.7 ma ma. 53. The transistor used in a portion of the TTL gate shown in the figure have a β = 00. The base emitter voltage of is 0.7V for a transistor in active region and 0.75V for a transistor in saturation. If the sink current I = ma and the output is at logic 0, then the current will be equal to.4k 5v k 0.65 ma ma ma..00 ma 54. The Boolean expression for the truth table shown is A B C F Page : 7

18 B (A + C) ( + ) B( A + ) ( + C) (A + ) ( + C) (A +C) ( + ) 55. Both transistors T and T2 show in the figure, have a threshold voltage of Volts. The device parameters and of T and T2 are, respectively, 36 A/ and 9 A/. The output voltage is 5V V 2 V 3 V 4 V 56. The present output of an edge triggered JK flip flop is logic 0. If J =, then cannot be determined will be logic 0 will be logic will race around 57. The given figure shows a ripple counter using positive edge triggered flip flops. If the present state of the counter is = 0, then its next state ( ) will be Page : 8

19 CLK > > > What memory address range is NOT represented by chip # and chip #2 in the figure to in this figure are the address lies and CS means Chip Select. 256 bytes - chip # bytes chip # FF 500 6FF Not used F900 FAFF F800 F9FF 59. The output of a linear time invariant system is related to its input by the following equation: ( ). The filter transfer function H( ) of such a system is given by ( + cos T) ( cos T) ( + cos T) ( 0.5 cos T) Page : 9

20 60. Match the following and choose the correct combination: Group Group 2 E. continuous and aperiodic signal. Fourier representation is continuous and aperiodic F. continuous and periodic signal 2. Fourier representation is discrete and aperiodic G. Discrete and aperiodic signal 3. Fourier representation is continuous and periodic H. Discrete and periodic signal 4. Fourier representation is discrete and periodic E 3, F 2, G 4, H E, F 3, G 2, H 4 E, F 2, G 3, H 4 E 2, F, G 4, H 3 6. A signal = sin ( n + ) is the input to a linear time invariant system having a frequency response H( ). If the output of the system Ax(n- ), then the most general form of H( ) will be. + for any arbitrary real. + 2 k for any arbitrary integer k. k. + 2 k for any arbitrary integer 62. For a signal the fourier transform is. Then the inverse Fourier transform of is given by 3x(3t) x(3t +2) 63. The polar diagram of a conditionally stable system for open loop gain K = is shown in the figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for lm Re GH plane Page : 20

21 K < 5 and In the derivation of expression for peak percent overshoot,, which one of the following conditions is NOT required? System is linear and time invariant. The system transfer function has a pair of complex conjugate poles and no zeroes There is no transportation delay in the system. The system has zero initial conditions. 65. Given the ideal operational amplifier circuit shown in the figure indicate the correct transfer characteristics assuming ideal diodes with zero cut in voltage. +0V -0V 2kΩ 2kΩ 0.5kΩ + 0V 8V + 5V 0V Page : 2

22 + 0V 5V + 8V 0V + 5V 5V + 5V 0V + 0V 5V + 5V 5V 66. A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively and 20 0 and 20 0 and and Page : 22

23 67. A double integrator plant, G(s) =, H(s) = is to be compensated to achieve the damping ratio ς=0.5, and an undamped natural frequency, = 5 rad/s. Which one of the following compensator (s) will be suitable? 68. An unity feedback system is given as, Indicate the correct root locus diagram. j X j j Page : 23

24 jω X 69. A MOS capacitor made using p type substrate is in the accumulation mode. The dominant charge in the channel is due to the presence of holes positively charged ions electrons negatively charged ions 70. A device with input and output is characterized by: (t). An FM signal with frequency deviation of 90 khz and modulating signal bandwidth of 5 khz is applied to this device. The bandwidth of the output signal is 370 khz 90 khz 380 khz 95 khz 7. A signal as shown in the figure is applied to a matched filter. Which of the following does represent the output of this matched filter? input 2 3 t Page : 24

25 Output 2 3 t Output 2 3 t Output t Output t Page : 25

26 72. Noise with uniform power spectral density of N 0 W/Hz is passed through a filter H(ω) = 2 exp ( jωt d ) followed by an ideal low pass filter of bandwidth B Hz. The output noise power in Watts is 2 N 0 B 4 N 0 B 8 N 0 B 6 N 0 B 73. A carrier is phase modulated (PM) with frequency deviation of 0 khz by single tone frequency of khz. If the single tone frequency is increased to 2 khz, assuming that phase deviation remains unchanged, the bandwidth of the PM signal is 2 khz. 22 khz 42 khz 44 khz 74. An output of a communication channel is a random variable v with the probability density function as shown in the figure The mean square value of v is Which one of the following does represent the electric field lines for the TE 02 mode in the crosssection of a hollow rectangular metallic waveguide? y y y x y x x x Page : 26

27 76. Characteristic impedance of a transmission line is 50Ω. Input impedance of the open circuited line is Z 0c = 00 + j50ω. When the transmission line is short circuited, then value of the input impedance will be 50Ω 00 + j50ω j.54ω j.54ω 77. Two identical and parallel dipole antennas are kept apart by a distance of in the H plane. They are fed with equal currents but the right most antenna has a phase shift of The radiation pattern is given as Common Data Question 78, 79, 80 Given, = 20 kω, = 0 ma, = 8V 20 V 2k Ω D G S 2M 2V Page : 27

28 78. and of the circuit are respectively 2 MΩ and 2 kω 2 MΩ and kω 79. and under DC conditions are respectively ma and 8.75 V ma and 5.00V infinity and 2 kω infinity and kω ma and.00 V ma and 7.50 V 80. Transconductance in milli Siemens(mS) and voltage gain of the amplifier are respectively.875 ms and ms and ms and ms and 6 Linked Answer Questions: Q. 8a to 85b Carry Two Marks Each Statement for Linked Answer Question 8a and 8b: Consider an 8085 microprocessor system 8. a. The following program starts at location 000H. LXI SP, 00FF LXI H, 070 MVI A, 20H SUB M The content of accumulator when the program counter reaches 009H is 20H 02H 00H FFH 8. b. If in addition following code exists from 09H onwards, ORI 40 H ADD M What will be the result in the accumulator after the last instruction is executed? 40H 20H 60H 42H Statement for Linked Answer Questions 82a and 82b: The dopen loop transfer function of a unity feedback system is given by G(s) = 82. a. The gain and phase crossover frequencies in rad/sec are, respectively and and and ma and V 82. b. Based on the above results, the gain and phase margins of the system will be 7.09 and db and and db and 87.5 Page : 28

29 Statement for Linked Answer Question 83a and 83b Asymmetric three level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels. 83. a. If the probability density function is divided into three regions as shown in the figure, the value of a in the figure is P(x) Region Region Region 3 a +a + +3 x 83. b. The quantization noise power for the quantization region between a and +a in the figure is Statement for Linked Answer Question 84a and 84b Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50W and a resistive load is shown in the figure. Page : 29

30 4 z 84. a. The value of the load resistance is 50Ω 200Ω /2 Load 2.5Ω 0Ω 84. b. The reflection coefficient is given by Statement for Linked Answer Question 85a and 85b A sequence x(n) has non-zero values as shown in the figure n 85. a. The sequence y(n) = will be n Page : 30

31 n n n 85. b. The Fourier transform of will be ] [cos2 Page : 3

ECE Branch GATE Paper 2004

ECE Branch GATE Paper 2004 Q. 1 30 Carry One Mark Each 1. Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph? Fig. Q.1 2. The equivalent inductance measured between the terminals