Q. No. 1 – 20 Carry One Mark Each
1. The order of the differential equation _{} is
(A) 1 (B) 2 (C) 3 (D) 4
2. The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd
Which of the above statements are correct?
(A) P and S (B) P and R (C) Q and S (D) Q and R
3. A function is given f(t) = sin^{2}t + cos2t. Which of the following is true?
(A) f has frequency components at 0 and 1/2p Hz
(B) f has frequency components at 0 and 1/p Hz
(C) f has frequency components at 1/2p and 1/p Hz
(D) f has frequency components at 0, 1/2p and 1/p Hz
4. A fully charged mobile phone with a 12V battery is good for a 10minute talktime. Assume that, during the talktime, the battery delivers a constant current of 2A and its voltage drops linearly from 12 V to 10V as shown in the figure. How much energy does the battery deliver during this talktime?
(A) 220J (B) 12kJ (C) 13.2kJ (D) 14.4kJ
5. In an ntype silicon crystal at room temperature, which of the following can have a concentration of
4 × 10^{19} cm^{−3} ?
4 × 10^{19} cm^{−3} ?
(A) Silicon atoms (B) Holes
(C) Dopant atoms (D) Valence electrons
6. The full form of the abbreviations TTL and CMOS in reference to logic families are
(A) Triple Transistor Logic and Chip Metal Oxide Semiconductor
(B) Tristate Transistor Logic and Chip Metal Oxide Semiconductor
(C) Transistor Transistor Logic and Complementary Metal Oxide Semiconductor
(D) Tristate Transistor Logic and Complementary Metal Oxide Silicon
7. The ROC of Ztransform of the discrete time sequence
x(n) = _{} is
(A) _{} (B) z > _{} (C) z < _{} (D) 2 < z < 3
8. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. When of the following compensators has such a magnitude plot?
(A) Lead compensator (B) Lag compensator
(C) PID compensator (D) Leadlag compensator
9. A white noise process X(t) with twosided power spectral density 1 × 10^{10} W/Hz is input to a filter whose magnitude squared response is shown below
The power of the output process Y(t) is given by
(A) 5 ´ 10^{}^{7} W (B) 1 ´ 10^{}^{6} W (C) 2 ´ 10^{}^{6} W (D) 1 ´ 10^{}^{5} W
10. Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?
(A) Only P has no cutofffrequency (B) Only Q has no cutofffrequency
(C) Only R has no cutofffrequency (D) all three have cutofffrequency
11. A fair coin is tossed 10times. What is the probability that ONLY the first two tosses will yield heads?
(A) _{} (B) _{} (C) _{} (D) _{}
12. If the power spectral density of stationary random process is a sinesquared function of frequency, the shape of its autocorrelation is
13. If f(z) = c_{0} + c_{1}z^{}^{1}, then _{} dz is given by
(A) 2pc_{1 }(B) 2p (1 + c_{0}) (C) 2pjc_{1} (D) 2pj (1 + c_{0})
14. In the interconnection of ideal sources shown in the figure, it is known that the 60V source is absorbing power
Which of the following can be the value of the current source _{}?
(A) 10A (B) 13A (C) 15A (D) 18A
15. The ratio of the mobility to the diffusion coefficient in a semiconductor has the units
(A) V^{−1} (B) em × V^{−1} (C) V × cm^{}^{1 }(D) V × s
16. In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is
(A) nonmaskable and nonvectored (B) maskable and nonvectored
(C) nonmaskable and vectored (D) maskable and vectored
17. If the transfer function of the following network is _{}_{}
The value of the load resistance R_{L} is
(A) R/4 (B) R/2 (C) R (D) 2R
18. Consider the system_{} with A = _{} and B = _{}where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?
(A) The system is completely state controllable for any nonzero values of p and q
(B) Only p=0 and q=0 result in controllability
(C) The system is uncontrollable for all values of p and q
(D) We cannot conclude about controllability from the given data
19. For a message signal m(t) = cos(2pf_{m}t) and carrier of frequency f_{c}, which of the following represents a single side band (SSB) signal?
(A) cos(2pf_{m}t) cos(2pf_{c}t) (B) cos(2pf_{c}t)
(C) cos[2p(f_{c} + f_{m})t] (D) [1 + cos(2pf_{m}t) ] cos(2pf_{c}t)
20. Two infinitely long wires carrying current are as shown in the figure below. One wire is in the yz plane and parallel to the yaxis. The other wise is in the xy plane and parallel to the xaxis. Which components of the resulting magnetic field are nonzero at the origin?
(A) x, y, z components (B) x, y components
(C) y, z components (D) x, z components
Q. No. 21 – 56 Carry Two Marks Each
21. Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities _{} and _{} respectively. What is the conditional probability P (X + Y = 2 X − Y = 0)?
(A) 0 (B) _{} (C) _{} (D) 1
22. The Taylor series expansion of _{}at x = p is given by
(A) 1 +_{} (B) 1 _{}
(C) 1 _{} (D) 1 +_{}
23. If a vector field _{} is related to another vector field _{} through _{}= Ñ ´ _{}, which of the following is true? Note: C and SC refer to any closed contour and any surface whose boundary is C.
(A) _{} (B) _{}
(C) _{} (D) _{}
24. Given that F(s) is the onesided Laplace transform of f(t), the Laplace transform of_{} is
(A) sF(s)  f(0) (B) _{} (C) _{} (D) _{}
25. Match each differential equation in Group I to its family of solution curves from
Group II.
Group  I Group  II
P. _{}_{} 1. Circles
Q. _{}_{} 2. Straight lines
R. _{}_{} 3. Hyperbolas
S. _{}_{}
(A) P2, Q3, R3, S1 (B) P1, Q3, R2, S1
(C) P2, Q1, R3, S3 (D) P3, Q2, R1, S2
26. The eigen values of the following matrix are_{}_{}
(A) 3,3 + 5j,6 − j (B) −6 + 5j,3 + j,3 − j
(C) 3 + j,3 − j,5 + j (D) 3, −1 + 3j, −1 − 3j
27. An AC source of RMS voltage 20V with internal impedance Z_{s} = (1 + 2j) W feeds a load of impedance Z_{t} = (7 + 4j) W in the figure below. The reactive power consumed by the load is
(A) 8VAR (B) 16AVR (C) 28VAR (D) 32VAR
28. The switch in the circuit shown was on position a for a long time, and is moved to position b at time t=0. The current i(t) for t>0 is given by
(A) 0.2e^{125t} u(t) mA (B) 20e^{1250t} u(t) mA
(C) 0.2e^{1250t} u(t) mA (D) 20e^{1000t} u(t) mA
29. In the circuit shown, what value of R_{L} maximizes the power delivered to R_{L}?
(A) 2.4W (B) _{}W (C) 4W (D) 6W
30. The time domain behavior of an RL circuit is represented by
L_{}+ Ri = V_{0}(1 +1Be^{Rt/L}sint) u (t).
For an initial current of i(0) =_{}, the steady state value of the current is given by
(A) i (t) ® _{} (B) i (t) ® _{}
(C) i (t) ® _{}(1 + B) (D) i (t) ® _{}(1 + B)
31. In the circuit below, the diode is ideal. The voltage V is given by
(A) min (V_{i},1) (B) max (V_{i},1) (C) min (−V_{i},1) (D) max (−V_{i},1)
32. Consider the following two statements about the internal conditions in an nchannel MOSFET operating in the active region
S1: The inversion charge decreases from source to drain
S2: The channel potential increases from source to drain
Which of the following is correct?
(A) Only S2 is true
(B) Both S1 and S2 are false
(C) Both S1 and S2 are true, but S2 is not a reason for S1
(D) Both S1 and S2 are true, and S2 is a reason for S1
33. In the following astable multivibrator circuit, which properties of v_{o}(t) depend on R_{2}?
(A) Only the frequency
(B) Only the amplitude
(C) Both the amplitude and the frequency
(D) Neither the amplitude nor the frequency
34. In the circuit shown below, the opamp is ideal, the transistor has V_{BE} = 0.6V and b = 150. Decide whether the feedback in the circuit is positive or negative and determine the voltage V at the output of the opamp
(A) Positive feedback, V=10 V (B) Positive feedback, V=0 V
(C) Negative feedback, V=5 V (D) Negative feedback, V=2 V
35. A small signal source v_{i} (t) = A cos20t + B sin10^{6} t is applied to a transistor amplifier as shown below. The transistor has b= 150 and h = 3kW. Which expression best approximates V_{0} (t)
(A) v_{0} (t) = 1500 ( A cos20t + B sin10^{6} t) (B) v_{0} (t) = 150 (A cos20t + B sin10^{6} t)
(C) v_{0} (t) = 1500B sin10^{6} t (D) v_{0} (t) = 150B sin10^{6} t
36. If X = 1 in the logic equation _{}_{}= 1, then
(A) Y=Z (B) Y = Z (C) Z=1 (D) 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 ExOR gate?
(A) 1 and 2 (B) 1 and 3 (C) 1 and 1 (D) 2 and 2
38. Refer to the NAND and NOR latches shown in the figure. The inputs (P_{1},P_{2} ) for both the latches are first made (0, 1) and then, after a few seconds, made (1, 1). The corresponding stable outputs (Q_{1}, Q_{2}) are
(A) NAND: first (0, 1) then (0, 1) NOR: first (1, 0) then (0, 0)
(B) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (1, 0)
(C) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (0, 0)
(D) NAND: first (1, 0) then (1, 1) NOR: first (0, 1) then (0, 1)
39. What are the counting stages (Q_{1}, Q_{2}) for the counter shown in the figure below?
(A) 11,10,00,11,10,.... (B) 01,10,11,00,01,....
(C) 00,11,01,10,00,.... (D) 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 statements
S1 : H(z) is a low pass filter
S2 : H(z) is a FIR filter
Which of the following is correct?
(A) Only S2 is true
(B) Both S1 and S2 are false
(C) Both S1 and S2 are true, and S2 is a reason for S1
(D) 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 graph
Which of the following four properties are possessed by the system?
BIBO: Bounded input gives a bounded output
Causal: The system is causal
LP: The system is low pass
LTI: The system is linear and time invariant
(A) Causal, LP (B) BIBO, LTI (C) BIBO, Causal, LTI (D) LP, LTI
42. The 4 point Discrete Fourier Transform (DFT) of a discrete time sequence {1, 0, 2, 3} is
(A) [0, 2 + 2j, 2, 2 2j] (B) [2, 2 + 2j, 6, 2  2j]
(C) [6, 1 3j, 2, 1 + 3j] (D) [6, 1 + 3j, 0, 1 3j]
43. The feedback configuration and the polezero locations of G(s) = _{} are shown below. The root locus for negative values of k, i.e. for −¥ < k < 0, has breakaway/break in points and angle of departure at pole P (with respect to the positive real axis) equal to
(A) ± 2 and 0ºError! Not a valid link. (B) ± 2 and 45º
(C) ± 3 and 0º (D) ± 3 and 45º
44. An LTI system having transfer function_{} and input x(t)=sin(t+1) is in steady state. The output is sampled at a ratew_{s} rad/s to obtain the final output {y(k)}. Which of the following is true?
(A) y(.) is zero for all sampling frequencies w_{s}
(B) y(.) is nonzero for all sampling frequencies w_{s}
(C) y(.) is nonzero for w_{s} >2, but zero for w_{s} >2
(D) y(.) is zero for w_{s} >2 but nonzero forw_{s} >2
45. The unit step response of an underdamped second order system has steady state value of 2. Which one of the following transfer functions has these properties?
(A) _{} (B) _{}
(C) _{} (D) _{}
46. A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean of X and 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true?
k

1

2

3

4

5

p(X = k)

0.1

0.2

0.4

0.2

0.1

(A) Both the student and the teacher are right
(B) Both the student and the teacher are wrong
(C) Both the student is wrong but the teacher is right
(D) The student is right but the teacher is wrong
47. A message signal given by
m(t) = _{} cosw_{1}t _{} sinw_{2}t
Is amplitude modulated with a carrier of frequencyw_{c} to generate s (t) = [1 + m(t)] cosw_{c}t
(A) 8.33% (B) 11.11% (C) 20% (D) 25%
48. A communication channel with AWGN operating at a signal to noise ratio SNR>>1 and bandwidth B has capacity C_{1}. If the SNR is doubled keeping B constant, the resulting capacity C_{2} is given by
(A) C_{2} » 2C_{1} (B) C_{2} » C_{1} + B (C) C_{2} » C_{1} + 2B (D) C_{2} » C_{1} + 0.3B
49. A magnetic field in air is measured to be _{}
What current distribution leads to this field? [Hint: The algebra is trivial in cylindrical coordinates.]
(A) _{} (B) _{}
(C) _{} (D) _{}
50. A transmission line terminates in two branches, each of length l/4, as shown. The branches are terminated by 50W loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Z_{1} as seen by the source
(A) 200W (B) 100W (C) 50W (D) 25W
Common Data Questions: 51 & 52
Consider a silicon pn junction at room temperature having the following parameters:
Doping on the nside = 1×10^{17} cm^{}^{3}
Depletion width on the nside = 0.1μm
Depletion width on the pside =1.0μm
Intrinsic carrier concentration = 1.4×10^{14} F. cm^{}^{1}
Thermal voltage = 26mV
Permittivity of free space = 8.85×10^{}^{14} F. cm^{}^{1}
Dielectric constant of silicon = 12
51. The built in potential of the junction
(A) is 0.70V (B) is 0.76V
(C) is 0.82V (D) cannot be estimated from the data given
52. The peak electric field in the device is
(A) 0.15 MV. cm^{}^{1}, directed from pregion to nregion
(B) 0.15 MV. cm^{}^{1}, directed from nregion to pregion
(C) 1.80 MV. cm^{}^{1}, directed from pregion to nregion
(D) 1.80 MV. cm^{}^{1}, directed from nregion to pregion
Common Data Questions: 53 & 54
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the tability of the closed loop system in the feedback configuration shown.
53. Which of the following statements is true?
(A) G(s) is an allpass filter
(B) G(s) has a zero in the righthalf plane
(C) G(s) is the impedance of a passive network
(D) G(s) is marginally stable
54. The gain and phase margins of G(s) for closed loop stability are
(A) 6dB and 180º (B) 3dB and 180º (C) 6dB and 90º (D) 3dB and 90º
Common Data Questions: 55 & 56
The amplitude of a random signal is uniformly distributed between 5V and 5V
55. If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5dB, the step size of the quantization is approximately
(A) 0.0333V (B) 0.05V (C) 0.0667V (D) 0.10V
56. If the positive values of the signal are uniformly quantized with a step size of 0.05V, and the negative values are uniformly quantized with a step size of 0.1V, the resulting signal to quantization noise ratio is approximately
(A) 46dB (B) 43.8dB (C) 42dB (D) 40dB
Linked Answer Questions: Q.57 to Q.60 Carry Two Marks Each
Statement for Linked Answer Questions: 57 & 58
Consider the CMOS circuit shown, where the gate voltage V_{G} of the nMOSFET is increased from zero, while the gate voltage of the pMOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the transconductance parameter and the (W/L) ratio, i.e. the quantity μ C_{ox} (W/ L) , is 1mA × V^{}^{2} .
57. For small increase in V_{G} beyond 1V, which of the following gives the correct description of the region of operation of each MOSFET?
(A) Both the MOSFETs are in saturation region
(B) Both the MOSFETs are in triode region
(C) nMOSFET is in triode and pMOSFET is in saturation region
(D) nMOSFET is in saturation and pMOSFET is in triode region
58. Estimate the output voltage V_{0} for V_{G} = 1.5V. [Hint: Use the appropriate current voltage equation for each MOSFET, based on the answer to Q.57]
(A) _{} (B) _{} (C) _{} (D) _{}
Statement for Linked Answer Questions: 59 & 60
Two products are sold from a vending machine, which has two push buttons P_{1 }and P_{2}. When a button is pressed, the price of the corresponding product is displayed in a 7segment display.
If no buttons are pressed, '0' is displayed, signifying 'Rs. 0'.
If only P_{1} is pressed, '2' is displayed, signifying 'Rs. 2'.
If only P_{2} is pressed, '5' is displayed, signifying 'Rs. 5'.
If both P_{1} and P_{2} are pressed, 'E' is displayed, signifying 'Error'.
The names of the segments in the 7segment 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 P_{1} and P_{2}, then which of the following is correct?
(A) g = _{}+ P_{2}, d = c + e (B) g = P_{1} + P_{2}, d = c + e
(C) g = _{} + P_{2}, e = b + c (D) g = P_{1} + P_{2}, e = b + c
60. What are the minimum numbers of NOT gates and 2input OR gates required to design the logic of the driver for this 7segment display?
(A) 3 NOT and 4 OR (B) 2 NOT and 4 OR
(C) 1 NOT and 3 OR (D) 2 NOT and 3 OR
0 comments:
Post a Comment
Comments : Read Them Or Add One to promote us