Electronics and Communication Gate 2018 Questions with Answer

Ques 53 GATE 2018


A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts. Which one of the following statements can be logically inferred from the information given in the above paragraph?

A

The culture and tradition of the local people will be influenced by the tourists.

B

The region will become crowded and polluted due to tourism.

C

The coral reefs are on the decline and could soon vanish.

D

Helicopter connectivity would lead to an increase in tourists coming to the region.


(d) is the correct answer.

Ques 54 GATE 2018


The ABCD matrix for a two-port network is defined by:

The parameter B for the given two-port network (in ohms, correct to two decimal places) is


(5) is the correct answer.

Ques 55 GATE 2018


For the circuit given in the figure, the voltage Vc (in volts) across the capacitor is

A

1.25√2sin(5t-0.25π)

B

1.25√2sin(5t-0.125π)

C

2.5√2sin(5t-0.25π)

D

2.5√2sin(5t-0.125π)


(c) is the correct answer.

Ques 56 GATE 2018


For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is


(0.31) is the correct answer.

Ques 57 GATE 2018


Consider the network shown below with R1=1Ω, R2=2Ω and R3=3Ω. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is


(8) is the correct answer.

Ques 58 GATE 2018


Let X1, X2, X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4 is the smallest among the four is


(0.25) is the correct answer.

Ques 59 GATE 2018


A random variable X takes values -0.5 and 0.5 with probabilities 1/4 and 3/4, respectively. The noisy observation of X is Y=X+Z where Z has uniform probability density over the interval (-1, 1). X and Z are independent. If the MAP rule based detector outputs

then the value of a (accurate to two decimal places) is


(-0.5) is the correct answer.

Ques 60 GATE 2018


Consider a white Gaussian noise process N(t) with two-sided power spectral density SN(f)=0.5 W/Hz as input to a filter with impulse response 0.5e-t2/2 (where t is in seconds) resulting in output Y(t). The power in Y(t) in watts is

A

0.11

B

0.22

C

0.33

D

0.44


(b) is the correct answer.

Ques 61 GATE 2018


A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30°. Which one of the following statements about the system is TRUE?

A

It has two more poles at 0.5∠30° and 4∠0°.

B

It is stable only when the impulse response is two-sided.

C

It has constant phase response over all frequencies.

D

It has constant phase response over the entire z-plane.


(b) is the correct answer.

Ques 62 GATE 2018


Let x(t) be a periodic function with period T=10. The Fourier series coefficients for this series are denoted by ak, that is x(t)=∑k=-∞akejk(2π/T)t. The same function x(t) can also be considered as a periodic function with period T'=40. Let bk be the Fourier series coefficients when period is taken as T'. If ∑k=-∞|ak|=16 then ∑k=-∞|bk| is equal to

A

256

B

64

C

16

D

4


(c) is the correct answer.

Ques 63 GATE 2018


The input 4sinc(2t) is fed to a Hilbert transformer to obtain y(t), as shown in the figure below: Here sinc(x)=sin(πx)/(πx).

The value (accurate to two decimal places) of ∫-∞|y(t)|2dt is


(8) is the correct answer.

Ques 64 GATE 2018


A band limited low-pass signal x(t) of bandwidth 5 kHz is sampled at a sampling rate fs. The signal x(t) is reconstructed using the reconstruction filter H(f) whose magnitude response is shown below:

The minimum sampling rate fS (in kHz) for perfect reconstruction of x(t) is


(13) is the correct answer.

Ques 65 GATE 2018


Let X[k]=k+1, 0≤k≤7 be 8-point DFT of a sequence x[n], where X[k]=∑n=0N-1x[n]e-j2πnk/N. The value (correct to two decimal places) of ∑n=03x[2n] is


(3) is the correct answer.

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