# EC GATE 2015 PAPER 01 (Test 3)

Tag: ec gate 2015 paper 01
Q.1
For the discrete-time system shown in the figure, the poles of the system transfer function are located at

A. 2, 3
B. 1/2, 3
C. 1/2, 1/3
D. 2, 1/3
Explaination / Solution:

We have the discrete time system as shown in figure below.

The circuit is minimized as

Hence, poles are at
z = 1/2, 1/3

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Q.2
A plant transfer function is given as  When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
A.

KP > K1 > 0

B.

2K1 > KP > 0

C.

2K1 < KP

D.

2K1 > KP

Explaination / Solution:

Given plant transfer function,

So, closed loop transfer function is

Therefore, characteristics equation is

For stability, we form the Routh array.

For stability, we must have

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Q.3
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude

A. h[n] is real for all n
B. h[n] is purely imaginary for all n
C. h[n] is real for only even n
D. h[n] is purely imaginary for only odd n
Explaination / Solution:

From the pole-zero plot, we obtain the transfer function as

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Q.4
The result of the convolution  is
A. x ( t + t0)
B. x ( t - t0)
C. x ( -t + t0)
D. x ( -t - t0)
Explaination / Solution:

From the convolution property,

Now, we replace t by -t to obtain

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Q.5
Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of Hϕ on r , where Hϕ is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor ?
A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.6
A vector is given by  Which one of the following statements is TRUE?
A. is solenoidal, but not irrotational
B. is irrotational, but not solenoidal
C. is neither solenoidal nor irrotational
D. is both solenoidal and irrotational
Explaination / Solution:

Given vector,

If divergence  then vector  is solenoidal. So, we obtain

Hence, it is solenoidal.
Again, if curl then  is irrotational. So, we obtain

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Q.7
In the given circuit, the values of V1 and V2 respectively are

A. 5 V, 25 V
B. 10 V, 30 V
C. 15 V, 35 V
D. 0 V, 20 V
Explaination / Solution:

By Nodal analysis

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Q.8
A function 1 – x2 + xis defined in the closed interval [-1, 1]. The value of x , in the open interval (-1, 1) for which the mean value theorem is satisfied, is
A. -1/2
B. -1/3
C. 1/3
D. 1/2
Explaination / Solution:

Lagrange’s mean value theorem states that if a function f(x) is continuous in close interval [a, b] and differentiable in open interval (a + b), then for point c in the interval, we may define

Since, polynomial function is always continuous and differentiable, so

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Q.9
The damping ratio of a series RLC circuit can be expressed as
A.
B.
C.
D.
Explaination / Solution:

Damping ratio is given by

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Q.10
Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let  and   be their complements. Which one of the following statements is FALSE?
A. P(A ∩ B) = P(A) P(B)
B.
C. P( A U B) = P(A) + P(B)
D.