Electronics and Communication Gate 2015 Set-2 Questions with Answer

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Ques 1 GATE 2015 SET-2

The bilateral Laplace transform of a function f(t) is is

(a-b)/s

e^s(a-b)/s

(e^-asa-b^-bs)/s

e^s(a-b)/s

(b) is the correct answer.

Ques 2 GATE 2015 SET-2

The value of x for which all the eigen-values of the matrix given below are real is

5+j

5−j

1−5j

1+5j

(b) is the correct answer.

Ques 3 GATE 2015 SET-2

Let f(z) = ^az+b⁄_cz+d. If f(z₁) = f(z₂) for all z₁ ≠ z₂, a=2, b=4 and c=5, then d should be equal to __________.

(10) is the correct answer.

Ques 4 GATE 2015 SET-2

The general solution of the differential equation ^dy⁄_dx = ^{1+cos 2y}⁄_{1−cos 2x} is

tan y − cot x = c (c is a constant)

tan x − cot y = c (c is a constant)

tan y + cot x = c (c is a constant)

tan x + cot y = c (c is a constant)

Ques 5 GATE 2015 SET-2

The magnitude and phase of the complex Fourier series coefficients a_k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers.

x(t) ∈ R

x(t) ∈ P

x(t) ∈ (C−R)

the information given is not sufficient to draw any conclusion about x(t)

(a) is the correct answer.

Ques 6 GATE 2015 SET-2

The voltage (V_c) across the capacitor (in Volts) in the network shown is __________.

(100) is the correct answer.

Ques 7 GATE 2015 SET-2

In the circuit shown, the average value of the voltage V_ab (in Volts) in steady state condition is __________.

(5) is the correct answer.

Ques 8 GATE 2015 SET-2

The 2-port admittance matrix of the circuit shown is given by

(d) is the correct answer.

Ques 9 GATE 2015 SET-2

An n-type silicon sample is uniformly illuminated with light which generates 10²⁰ electron-hole pairs per cm³ per second. The minority carrier lifetime in the sample is 1 μs. In the steady state, the hole concentration in the sample is approximately 10^x, where x is an integer. The value of x is __________.

(14) is the correct answer.

Ques 10 GATE 2015 SET-2

A piece of silicon is doped uniformly with phosphorous with a doping concentration of 10¹⁶/cm³. The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is 1.6 × 10⁻¹⁹ C. The conductivity (in S cm⁻¹) of the silicon sample at 300 K is __________.

(1.92) is the correct answer.

Ques 11 GATE 2015 SET-2

If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period T?

RC ≪≪ T

RC = 0.35 T

RC ≈ T

RC ≫≫ T

(d) is the correct answer.

Ques 12 GATE 2015 SET-2

In the circuit shown, V₀ = V_0A for switch SW in position A and V₀ = V_0B for SW in position B. Assume that the opamp is ideal. The value of ^V_0B⁄_{V_0A} is __________.

(1.5) is the correct answer.

Ques 13 GATE 2015 SET-2

In the bistable circuit shown, the ideal opamp has saturation levels of ±5 V. The value of R₁ (in kΩ) that gives a hysteresis width of 500 mV is __________.

(1) is the correct answer.

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