gate paper ece 2009

7/30/2019 gate paper ece 2009

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Electronics and Communication Engg - 2009

Full Paper

1. The order of the differential equation (d2y/dt2) + (dy/dt)3 + y4 = e-t is

1) 1 2) 2 3) 3 4) 4

2. The Fourier series of a real periodic function has onlyP. Cosine terms if it is evenQ. Sine terms if it is evenR. Cosine terms if it is oddS. Sine terms if it is oddWhich of the above statements are correct?

1) P and S

2) P and R

3) Q and S

4) Q and R

3. A function is given f (t) = sin2 t + cos 2t. Which of the following is true?

1) f has frequency components at 0 and 1/2 Hz

2) f has frequency components at 0 and 1/ Hz

3) f has frequency components at 1/2 and 1/ Hz4) f has frequency components at 0, 1/2 and 1/ Hz

4. A fully charged mobile phone with a 12V battery is good for a 10 minute talk-time. Assumethat, during the talk-time, the battery delivers a constant current of 2A and its voltagedrops linearly from 12 V to 10 V as shown in the figure. How much energy does the batterydeliver during this talk-time?

1) 220J

2) 12kJ

3) 13.2kJ

4) 14.4kJ

5. In an n-type silicon crystal at room temperature, which of the following can have a

concentration of 4 x 1019cm-3 ?

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1) Silicon atoms

2) Holes

3) Dopant atoms

4) Valence electrons

6. The full form of the abbreviations TTL and CMOS in reference to logic families are1) Triple Transistor Logic and Chip Metal Oxide Semiconductor

2) Tristate Transistor Logic and Chip Metal Oxide Semiconductor

3) Transistor Transistor Logic and Complementary Metal Oxide Semiconductor

4) Tristate Transistor Logic and Complementary Metal Oxide Silicon

7. The ROC of Z-transform of the discrete time sequence x(n) = (1/3)n u(n) - (1/2)n u(-n -1)is

1) (1/3) < |z| < (1/2)

2) |z| > (1/2)3) |z| < (1/3)

4) 2 < |z| < 3

8. The magnitude plot of a rational transfer function G(s) with real coefficients is shownbelow. When of the following compensators has such a magnitude plot?

1) Lead compensator

2) Lag compensator

3) PID compensator

4) Lead-lag compensator

9. A white noise process X(t) with two-sided power spectral density 1 x 10 -10 W/Hz is input toa filter whose magnitude squared response is shown below

The power of the output process Y(t) is given by

1) 5 x 10-7 W2) 1 x 10-6 W



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3) 2 x 10-6 W

4) 1 x 10-5 W

10. Which of the following statements is true regarding the fundamental mode of the metallicwaveguides shown?

1) Only P has no cutoff-frequency

2) Only Q has no cutoff-frequency

3) Only R has no cutoff-frequency

4) all three have cutoff-frequency

11. A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses willyield heads?

1) (1/2)2

2) 10C2 (1/2)2

3) (1/2)10

4) 10C2 (1/2)10

12. If the power spectral density of stationary random process is a sine-squared function of

frequency, the shape of its autocorrelation is1)

2)

3)

4)



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13.

If f (z) = c0 + c1z-1, then is given by

1) 2c1

2) 2(1 + c0)

3) 2jc1

4) 2j(1 + c0)

14. In the interconnection of ideal sources shown in the figure, it is known that the 60V sourceis absorbing power

Which of the following can be the value of the current source l ?

1) 10A 2) 13A 3) 15A 4) 18A

15. The ratio of the mobility to the diffusion coefficient in a semiconductor has the units

1) V-1

2) em . V-1

3) V . cm-14) V . s

16. In a microprocessor, the service routine for a certain interrupt starts from a fixed locationof memory which cannot be externally set, but the interrupt can be delayed or rejected.Such an interrupt is

1) non-maskable and non-vectored

2) maskable and non-vectored

3) non-maskable and vectored

4) maskable and vectored

17. If the transfer function of the following network is (V0(s))/(Vi(s)) = 1/(2 + s CR)

The value of the load resistance RL is

1) R/4 2) R/2 3) R 4) 2R



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18. Consider the system (dx/dt) = Ax + Bu with A = and B = where p and q are

arbitrary real numbers. Which of the following statements about the controllability of thesystem is true?

1) The system is completely state controllable for any nonzero values of p and q

2) Only p = 0 and q = 0 result in controllability

3) The system is uncontrollable for all values of p and q

4) We cannot conclude about controllability from the given data

19. For a message signal m (t) = cos (27f mt) and carrier of frequency fc, which of the

following represents a single side band (SSB) signal?

1) cos (2fmt) cos (2fct)

2) cos (2fct)

3) cos [2(fc + tm)t]

4) [1 + cos(2fmt)] cos (2fct)

20. Two infinitely long wires carrying current are as shown in the figure below. One wire is inthe y-z plane and parallel to the y-axis. The other wise is in the x-y plane and parallel tothe x-axis. Which components of the resulting magnetic field are non-zero at the origin?

1) x, y, z components

2) x, y components

3) y, z components

4) x, z components

21. Consider two independent random variables X and Y with identical distributions. Thevariables X and Y take values 0, 1 and 2 with probabilities 1/2, 1/4 and 1/4 respectively.What is the conditional probability P(X + Y = 2 | X - Y = 0) ?

1) 0 2) 1/16 3) 1/6 4) 1

22. The Taylor series expansion of (sin x)/(x - ) at x = is given by

1) 1 + (x - )2/3! + .....

2) - 1 - (x - )2/3! + .....

3) 1 - (x - )2/3! + .....

4) - 1 + (x - )2/3! + .....



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23. If a vector field is related to another vector field through = x , which of the

following is true? Note: C and SC refer to any closed contour and any surface whose

boundary is C.

1)

2)

3)

4)

24. Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of

is

1) s F(s) - f(0)

2) (1/s)F(s)

3)

4) (1/s)[F(s) - f(0)]

25. Match each differential equation in Group I to its family of solution curves from Group II.Group I Group II

P. (dy/dx) = (y/x) 1. Circles

Q. (dy/dx) = -(y/x) 2. Straight linesR. (dy/dx) = (x/y) 3. HyperbolasS. (dy/dx) = -(x/y)

1) P-2, Q-3, R-3, S-1

2) P-1, Q-3, R-2, S-1

3) P-2, Q-1, R-3, S-3

4) P-3, Q-2, R-1, S-2

26. The eigen values of the following matrix are

1) 3, 3 + 5j, 6 - j



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2) -6 + 5j, 3 + j, 3 - j

3) 3 + j, 3 - j, 5 + j

4) 3, -1 + 3j, -1 - 3j

27. An AC source of RMS voltage 20V with internal impedance ZS = (1 + 2j) feeds a load of

impedance ZL = (7 + 4j) in the figure below. The reactive power consumed by the load is

1) 8VAR

2) 16VAR

3) 28VAR

4) 32VAR

28. The switch in the circuit shown was on position a for a long time, and is moved to positionb at time t = 0. The current i(t) for t > 0 is given by

1) 0.2e-125tu (t) mA

2) 20e-1250tu (t) mA

3) 0.2e-1250tu (t) mA

4) 20e-1000tu (t) mA

29. In the circuit shown, what value of RL maximizes the power delivered to RL?

1) 2.4



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2) (8/3)

3) 4

4) 6

30. The time domain behavior of an RL circuit is represented by

L(di/dt) + Ri = V0(1 + Be-Rt/L

sin t) u (t).For an initial current of i (0) = (V0/R) , the steady state value of the current is given by

1) i(t) (V0/R)

2) i(t) (2V0/R)

3) i(t) (V0/R)(1 + B)

4) i(t) (2V0/R)(1 + B)

31. In the circuit below, the diode is ideal. The voltage V is given by

1) min (Vi, 1)

2) max (Vi, 1)

3) min (-Vi, 1)

4) max (-Vi, 1)

32. Consider the following two statements about the internal conditions in an n-channelMOSFET operating in the active regionS1: The inversion charge decreases from source to drainS2: The channel potential increases from source to drainWhich of the following is correct?

1) Only S2 is true

2) Both S1 and S2 are false

3) Both S1 and S2 are true, but S2 is not a reason for S14) Both S1 and S2 are true, and S2 is a reason for S1

33. In the following astable multivibrator circuit, which properties of V0(t) depend on R2?



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1) Only the frequency

2) Only the amplitude

3) Both the amplitude and the frequency

4) Neither the amplitude nor the frequency

34. In the circuit shown below, the op-amp is ideal, the transistor has VBE = 0.6V and = 150.Decide whether the feedback in the circuit is positive or negative and determine thevoltage V at the output of the op-amp

1) Positive feedback, V = 10 V

2) Positive feedback, V = 0 V

3) Negative feedback, V = 5 V

4) Negative feedback, V = 2 V

35. A small signal source Vi (t) = A cos 20t + B sin 106t is applied to a transistor amplifier asshown below. The transistor has = 150 and h ie = 3k. Which expression best

approximates V0 (t)



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1) V0 (t) = -1500 (A cos 20t + B sin 106t)

2) V0 (t) = -150 (A cos 20t + B sin 106t)

3) V0 (t) = -1500B sin 106t

4) V0

(t) = -150B sin 106t

36. If X = 1 in the logic equation [X + Z{ + ( + X )}] { + (X + Y)} = 1, then

1) Y = Z

2) Y =

3) Z = 1

4) Z = 0

37. What are the minimum number of 2 to 1 multiplexers required to generate a 2 input AND

gate and a 2 input Ex-OR gate?1) 1 and 2

2) 1 and 3

3) 1 and 1

4) 2 and 2

38. Refer to the NAND and NOR latches shown in the figure. The inputs (P1, P2) for both

the latches are first made (0, 1) and then, after a few seconds, made (1, 1). Thecorresponding stable outputs (Q1, Q2) are

1) NAND: first (0, 1) then (0, 1) NOR: first (1, 0) then (0, 0)

2) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (1, 0)3) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (0, 0)



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4) NAND: first (1, 0) then (1, 1) NOR: first (0, 1) then (0, 1)

39. What are the counting stages (Q1, Q2) for the counter shown in the figure below?

1) 11, 10, 00, 11, 10, ....2) 01, 10, 11, 00, 01, ....

3) 00, 11, 01, 10, 00, ....

4) 01, 10, 00, 01, 10, ....

40. A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statementsS1 : H (z) is a low pass filterS2 : H (z) is a FIR filterWhich of the following is correct?

1) Only S2 is true

2) Both S1 and S2 are false

3) Both S1 and S2 are true, and S2 is a reason for S1

4) Both S1 and S2 are true, but S2 is not a reason for S1

41. Consider a system whose input x and output y are related by the equation

y (t) =

Where h(t) is shown in the graphWhich of the following four properties are possessed by the system?BIBO: Bounded input gives a bounded outputCausal: The system is causalLP: The system is low passLTI: The system is linear and time invariant



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1) Causal, LP

2) BIBO, LTI

3) BIBO, Causal, LTI

4) LP, LTI

42. The 4 point Discrete Fourier Transform (DFT) of a discrete time sequence {1, 0, 2, 3} is1) [0, - 2 + 2j, 2, - 2 - 2j]

2) [2, 2 + 2j, 6, 2 - 2j]

3) [6, 1 - 3j, 2, 1 + 3j]

4) [6, - 1 + 3j, 0, - 1 - 3j]

43. The feedback configuration and the pole-zero locations of G(s) = (s2 - 2s + 2)/(s2 + 2s + 2)are shown below. The root locus for negative values of k, i.e. for k 0, - < k < 0,has breakaway/break in points and angle of departure at pole P (with respect to the

positive real axis) equal to

1) 2 and 0

2) 2 and 45

3) 3 and 0

4) 3 and 45

44. An LTI system having transfer function (s2 + 1)/(s2 + 2s + 1) and input x(t) = sin(t + 1) isin steady state. The output is sampled at a rate S rad/s to obtain the final output {y (k)}.

Which of the following is true?

1) y(.) is zero for all sampling frequenciess

2) y(.) is nonzero for all sampling frequencies s

3) y(.) is nonzero for s > 2, but zero for s > 24) y(.) is zero fors > 2 but nonzero for s > 2

45. The unit step response of an under-damped second order system has steady state valueof -2. Which one of the following transfer functions has these properties?

1) (-2.24)/(s2 + 2.59s + 1.12)

2) (-3.82)/(s2 + 1.91s + 1.91)

3) (-2.24)/(s2 - 2.59s + 1.12)

4)(-3.82)/(s

2

- 1.91s + 1.91)



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46. A discrete random variable X takes values from 1 to 5 with probabilities as shown in thetable. A student calculates the mean of X and 3.5 and her teacher calculates the varianceof X as 1.5. Which of the following statements is true?

k 1 2 3 4 5P(X = k) 0.1 0.2 0.4 0.2 0.1

1) Both the student and the teacher are right

2) Both the student and the teacher are wrong

3) Both the student is wrong but the teacher is right

4) The student is right but the teacher is wrong

47. A message signal given bym(t) = (1/2) cos 1t - (1/2) sin 2t

Is amplitude modulated with a carrier of frequency c to generate

s(t) = [1 + m(t)] cos ct

1) 8.33%

2) 11.11%

3) 20%

4) 25%

48. A communication channel with AWGN operating at a signal to noise ratio SNR>>1 andbandwidth B has capacity C1. If the SNR is doubled keeping B constant, the resulting

capacity C2 is given by

1) C2 2C12) C2 C1 + B

3) C2 C1 + 2B

4) C2 C1 + 0.3B

49. A magnetic field in air is measured to be

= B0 ((x/(x2 + y2)) - (y/(x2 + y2)) )

What current distribution leads to this field? [Hint: The algebra is trivial in cylindricalcoordinates.]

1) = (B0 /0)(1/(x2 + y2)), r 0

2) = (B0 /0)(2/(x2 + y2)), r 0

3) = 0, r 0

4) = (B0 /0)(3/(x2 + y2)), r 0

50. A transmission line terminates in two branches, each of length/4, as shown. Thebranches are terminated by 50 loads. The lines are lossless and have thecharacteristic impedances shown. Determine the impedance Z1 as seen by the source



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1) 200

2) 100

3) 50

4) 25

Consider a silicon p-n junction at room temperature having the following parameters:

Doping on the n-side = 1 x 1017cm-3Depletion width on the n-side = 0.1m

Depletion width on the p-side =1.0mIntrinsic carrier concentration = 1.4 x 1014F. cm-1Thermal voltage = 26mV

Permittivity of free space = 8.85 x 10-14F. cm-1Dielectric constant of silicon = 12

51. The built in potential of the junction

1) is 0.70V

2) is 0.76V

3) is 0.82V

4) cannot be estimated from the data given

52. The peak electric field in the device is

1) 0.15 MV.cm-1, directed from p-region to n-region

2) 0.15 MV.cm-1, directed from n-region to p-region

3) 1.80 MV.cm-1, directed from p-region to n-region

4) 1.80 MV.cm-1, directed from n-region to p-region

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interestedin the stability of the closed loop system in the feedback configuration shown.

53. Which of the following statements is true?



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1) G(s) is an all-pass filter

2) G(s) has a zero in the right-half plane

3) G(s) is the impedance of a passive network

4) G(s) is marginally stable

54. The gain and phase margins of G(s) for closed loop stability are1) 6dB and 180

2) 3dB and 180

3) 6dB and 90

4) 3dB and 90

The amplitude of a random signal is uniformly distributed between -5V and 5V

55. If the signal to quantization noise ratio required in uniformly quanting the signal is 43.5dB,the step size of the quantization is approximately

1) 0.0333V2) 0.05V

3) 0.0667V

4) 0.10V

56. If the positive values of the signal are uniformly quantized with a step size of 0.05V, andthe negative values are uniformly quantized with a step size of 0.1V, the resulting signal toquantization noise ratio is approximately

1) 46dB

2) 43.8dB3) 42dB

4) 40dB

Consider the CMOS circuit shown, where the gate voltage VG of the n-MOSFET isincreased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V.Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and theproduct of the transconductance parameter and the (W/L) ratio, i.e. the quantity Cox

(W/L), is 1mA . V2.

57. For small increase in VG beyond 1V, which of the following gives the correct description of

the region of operation of each MOSFET?

1) Both the MOSFETs are in saturation region



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2) Both the MOSFETs are in triode region

3) n-MOSFET is in triode and p-MOSFET is in saturation region

4) n-MOSFET is in saturation and p-MOSFET is in triode region

58. Estimate the output voltage V0 for VG = 1.5V.

[Hint: Use the appropriate current voltage equation for each MOSFET, based on theanswer to above Question]

1) 4 - (1/2)V

2) 4 + (1/2)V

3) 4 - (3/2)V

4) 4 + (3/2)V

Two products are sold from a vending machine, which has two push buttons P1 and P2.

When a button is pressed, the price of the corresponding product is displayed in a 7-

segment display.If no buttons are pressed, '0' is displayed, signifying 'Rs. 0'.If only P1 is pressed, '2' is displayed, signifying 'Rs. 2'.

If only P2 is pressed, '5' is displayed, signifying 'Rs. 5'.

If both P1 and P2 are pressed, 'E' is displayed, signifying 'Error'.

The names of the segments in the 7-segment display, and the glow of the display for '0','2', '5' and 'E', are shown below

Consider(i) push button pressed/not pressed is equivalent to logic 1/0 respectively(ii) a segment glowing/not glowing in the display is equivalent to logic 1/0 respectively

59. If segments a to g are considered as functions of P1 and P2, then which of the following is

correct?

1) g = 1 + P2, d = c + e

2) g = P1 + P2, d = c + e

3) g = + P2, e = b + c4) g = P1 + P2, e = b + c

60. What are the minimum numbers of NOT gates and 2-input OR gates required to designthe logic of the driver for this 7-segment display?

1) 3 NOT and 4 OR

2) 2 NOT and 4 OR

3) 1 NOT and 3 OR

4) 2 NOT and 3 OR



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Answer Key

1) 2 2) 1 3) 2 4) 3 5) 3 6) 3 7) 1 8) 4 9) 2 10) 1

11) 3 12) 2 13) 2 14) 1 15) 1 16) 4 17) 3 18) 3 19) 3 20) 4

21) 3 22) 4 23) 2 24) 2 25) 1 26) 4 27) 1 28) 2 29) 3 30) 1

31) 4 32) 4 33) 1 34) 4 35) 4 36) 4 37) 1 38) 3 39) 1 40) 1

41) 2 42) 4 43) 2 44) 1 45) 2 46) 2 47) 3 48) 2 49) 3 50) 4

51) 2 52) 2 53) 3 54) 3 55) 3 56) 4 57) 1 58) 3 59) 2 60) 4

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