Electronics and Communication Gate 2014 Set-4 Questions with Answer

Ques 14 GATE 2014 SET-4

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4^th order all-pole system?

−80 dB/decade

−40 dB/decade

+40 dB/decade

+80 dB/decade

(a) is the correct answer.

Ques 15 GATE 2014 SET-4

For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

(b) is the correct answer.

Ques 16 GATE 2014 SET-4

The state transition matrix φ(t) of a system is

[t 1; 1 0]

[1 0; t 1]

[0 1; 1 t]

[1 t; 0 1]

(d) is the correct answer.

Ques 17 GATE 2014 SET-4

Consider a transfer function G_p(s) = (ps²+3ps−2)/(s²+(3+p)s+(2−p)) with p a positive real parameter. The maximum value of p until which G_p remains stable is ________.

(2) is the correct answer.

Ques 18 GATE 2014 SET-4

The characteristic equation of a unity negative feedback system is 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure. The constant damping ratio line, for ξ=0.5, intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________.

(0.37) is the correct answer.

Ques 19 GATE 2014 SET-4

In the circuit shown in the figure, if C = 0, the expression for Y is

Y = AB̅ + A̅B

Y = A + B

Y = A̅ + B̅

Y = AB

(y = ab̅ + a̅b) is the correct answer.

Ques 20 GATE 2014 SET-4

The output (Y) of the circuit shown in the figure is

A + B + C

C̅A + C̅B + CA

A̅ + B̅ + C̅

ABC

(a + b + c) is the correct answer.

Ques 21 GATE 2014 SET-4

An 8-to-1 multiplexer is used to implement a logical function Y as shown in the figure. The output Y is given by

Y = AB̅C + AC̅D

Y = A̅BC + AB̅D

Y = ABC̅ + A̅CD

Y = A̅B̅D + AB̅C

(y = abc̅ + a̅cd) is the correct answer.

Ques 22 GATE 2014 SET-4

A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is 12 ns and the sum-propagation delay of each FA is 15 ns. The worst case delay (in ns) of this 16-bit adder will be __________.

(195) is the correct answer.

Ques 23 GATE 2014 SET-4

For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 mV/m. Given that intrinsic impedance of the free space is 120π Ω, the magnitude of average power density due to this antenna at a distance of 2 km from the antenna (in nW/m²) is ____.

(47.7) is the correct answer.

Ques 24 GATE 2014 SET-4

Match column A with column B.

Column A	Column B
1. Point electromagnetic source	R. Isotropic
2. Dish antenna	P. Highly directional
3. Yagi-Uda antenna	Q. End fire

1 → P, 2 → Q, 3 → R

1 → R, 2 → P, 3 → Q

1 → Q, 2 → P, 3 → R

1 → R, 2 → Q, 3 → P

(b) is the correct answer.

Ques 25 GATE 2014 SET-4

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let ψ_A and ψ_B be the electrostatic potentials at A and B, respectively. The value of ψ_B – ψ_A in Volts is ________.

(-15) is the correct answer.

Ques 26 GATE 2014 SET-4

Given F = ẑa + x̂a + ŷa. If S represents the portion of the sphere x² + y² + z² = 1 for z ≥ 0, then ∫∫_S ∇ × F · ds is______________.

(3.14) is the correct answer.

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