Electronics and Communication Gate 2015 Set-2 Questions with Answer

Ques 40 GATE 2015 SET-2

Assuming that the opamp in the circuit shown below is ideal, the output voltage V₀ (in volts) is __________.

(11) is the correct answer.

Ques 41 GATE 2015 SET-2

For the voltage regulator circuit shown, the input voltage (V_in) is 20 V ± 20% and the regulated output voltage (V_out) is 10 V. Assume the opamp to be ideal. For a load R_L drawing 200 mA, the maximum power dissipation in Q₁ (in Watts) is __________.

(2.8) is the correct answer.

Ques 42 GATE 2015 SET-2

In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical parameters with β ≫≫ 1. The open circuit small signal voltage gain is approximately __________.

(-1) is the correct answer.

Ques 43 GATE 2015 SET-2

Input x(t) and output y(t) of an LTI system are related by the differential equation y″″(t) − y″(t) − 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

¹⁄₅e^3tu(−t) + ¹⁄₅e^−2tu(−t)

−¹⁄₅e^3tu(−t) + ¹⁄₅e^−2tu(−t)

¹⁄₅e^3tu(−t) − ¹⁄₅e^−2tu(t)

−¹⁄₅e^3tu(−t) − ¹⁄₅e^−2tu(t)

Ques 44 GATE 2015 SET-2

Consider two real sequences with time-origin marked by the bold value, x₁[n] = {1, 2, 3, 0}, x₂[n] = {1, 3, 2, 1}. Let X₁(k) and X₂(k) be 4-point DFTs of x₁[n] and x₂[n] respectively. Another sequence x₃[n] is derived by taking 4-point inverse DFT of X₃(k) = X₁(k)X₂(k). The value of x₃[2] is __________.

(11) is the correct answer.

Ques 45 GATE 2015 SET-2

Let x(t) = α s(t) + s(−t) with s(t) = β e^−4tu(t), where u(t) is unit step function. If the bilateral Laplace transform of x(t) is X(s) = ¹⁶⁄_s²−16, −4 < Re{s} < 4, then the value of α − β is __________.

(-2) is the correct answer.

Ques 46 GATE 2015 SET-2

The state variable representation of a system is given as

The response y(t) is

sin(t)

1−e^t

1−cos(t)

(d) is the correct answer.

Ques 47 GATE 2015 SET-2

The output of a standard second-order system for a unit step input is given as y(t) = 1 − ²⁄_√3e^−tcos(√3t − ^π⁄₆). The transfer function of the system is

²⁄_{(s+2)(s+√3)}

¹⁄_s²+2s+1

³⁄_s²+2s+3

⁴⁄_s²+2s+4

(d) is the correct answer.

Ques 48 GATE 2015 SET-2

The transfer function of a mass-spring-damper system is given by G(s) = ¹⁄_Ms²+Bs+K. The frequency response data for the system are given in the following table.

The unit step response of the system approaches a steady state value of __________.

(0.118) is the correct answer.

Ques 49 GATE 2015 SET-2

A zero mean white Gaussian noise having power spectral density ^N₀⁄₂ is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t=4 is

³⁄₂A² N₀

³⁄₄A² N₀

A² N₀

¹⁄₂A² N₀

(d) is the correct answer.

Ques 50 GATE 2015 SET-2

{X_n}_n=−∞^n=∞ is an independent and identically distributed (i.i.d.) random process with X_n equally likely to be +1 or −1. {Y_n}_n=−∞^n=∞ is another random process obtained as Y_n = X_n + 0.5 X_n−1. The autocorrelation function of {Y_n}_n=−∞^n=∞, denoted by R_Y[k], is

(b) is the correct answer.

Ques 51 GATE 2015 SET-2

Consider a binary, digital communication system which uses pulses g(t) and −g(t) for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?

(a) is the correct answer.

Ques 52 GATE 2015 SET-2

Let X ∈ {0,1} and Y ∈ {0,1} be two independent binary random variables. If P(X=0)=p and P(Y=0)=q, then P(X+Y ≥ 1) is equal to

pq + (1−p)(1−q)

p(1−q)

1−pq

(d) is the correct answer.

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