Electronics and Communication Gate 2013 Set-1 Questions with Answer

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Ques 53 GATE 2013 SET-1

Consider the following figure with a 2A current source, 5Ω, 10V voltage source, 1Ω and 2Ω resistors.

The current I_S in Amps in the voltage source, and voltage V_S in Volts across the current source respectively, are

13, −20

8, −10

−8, 20

−13, 20

(d) is the correct answer.

Ques 54 GATE 2013 SET-1

Consider the following figure with a 2A current source, 5Ω, 10V voltage source, 1Ω and 2Ω resistors. The current in the 1Ω resistor in Amps is

3.33

(d) is the correct answer.

Ques 55 GATE 2013 SET-1

Two systems with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

product of h₁(t) and h₂(t)

sum of h₁(t) and h₂(t)

convolution of h₁(t) and h₂(t)

subtraction of h₂(t) from h₁(t)

Ques 56 GATE 2013 SET-1

The impulse response of a system is h(t) = tu(t). For an input u(t−1), the output is

t²/2 u(t)

t(t−1)/2 u(t−1)

(t−1)²/2 u(t−1)

(t²−1)/2 u(t−1)

Ques 57 GATE 2013 SET-1

For a periodic signal v(t) = 30 sin 10t + 10 cos 30t + 6 sin(500t + π/4), the fundamental frequency in rad/s is

100

300

500

1500

(a) is the correct answer.

Ques 58 GATE 2013 SET-1

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

5 kHz

12 kHz

15 kHz

20 kHz

(a) is the correct answer.

Ques 59 GATE 2013 SET-1

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

All the poles of the system must lie on the left side of the jω axis.

Zeros of the system can lie anywhere in the s-plane.

All the poles must lie within |s| = 1.

All the roots of the characteristic equation must be located on the left side of the jω axis.

Ques 60 GATE 2013 SET-1

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is

u(t)

tu(t)

t²/2 u(t)

e^−tu(t)

Ques 61 GATE 2013 SET-1

Let g(t) = e^−πt², and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is

e^−πf²

e^−πf²/2

e^−π|f|

e^−2πf²

(b) is the correct answer.

Ques 62 GATE 2013 SET-1

The impulse response of a continuous time system is given by h(t) = δ(t−1) + δ(t−3). The value of the step response at t = 2 is

(b) is the correct answer.

Ques 63 GATE 2013 SET-1

A system is described by the differential equation
d²y/dt² + 5(dy/dt) + 6y(t) = x(t).
Let x(t) be a rectangular pulse given by x(t) = 1 for 0 < t < 2 and 0 otherwise.
Assuming that y(0) = 0 and dy/dt = 0 at t = 0, the Laplace transform of y(t) is

e^−2s/(s(s+2)(s+3))

(1−e^−2s)/(s(s+2)(s+3))

e^−2s/(s(s+2)(s+3))

(1−e^−2s)/(s+2)(s+3)

(b) is the correct answer.

Ques 64 GATE 2013 SET-1

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes −2y(t) for t > 0, we need to

change the initial condition to −y(0) and the forcing function to 2x(t)

change the initial condition to 2y(0) and the forcing function to −x(t)

change the initial condition to 2jy(0) and the forcing function to 2jx(t)

change the initial condition to −2y(0) and the forcing function to −2x(t)

(d) is the correct answer.

Ques 65 GATE 2013 SET-1

The DFT of a vector [a b c d] is the vector [α β γ δ]. Consider the product,

The DFT of the vector [p q r s] is a scaled version of

[α² β² γ² δ²]

[α β γ δ]

[αβ + βδ + δγ + γα]

[α β γ δ]

(a) is the correct answer.

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