EC GATE 2015 PAPER 01 - Online Test
Q1. The result of the convolution 
is
is
Answer : Option D
Explaination / Solution:
From the convolution property,
Now, we replace t by -t to obtain
Q2. In the given circuit, the values of V1 and V2 respectively are
Answer : Option A
Explaination / Solution:
By Nodal analysis
Q3. A function 1 – x2 + x3 is 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
Answer : Option B
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
Q4. The damping ratio of a series RLC circuit can be expressed as
Answer : Option C
Explaination / Solution:
Damping ratio is given by
Q5. The polar plot of the transfer function 
will be in the
will be in the
Answer : Option A
Explaination / Solution:
Q6. Negative feedback in a closed-loop control system DOES NOT
Answer : Option B
Explaination / Solution:
Negative feedback in closed-loop control system does not reduce bandwidth.
Q7. 
For the discrete-time system shown in the figure, the poles of the system transfer function are located at
Answer : Option C
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
Q8. 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
When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
Answer : Option A
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
Q9. 
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
Answer : Option A
Explaination / Solution:
From the pole-zero plot, we obtain the transfer function as
Q10. 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?
and be their complements. Which one of the following statements is FALSE?
Answer : Option C
Explaination / Solution:
A and B are two independent events with probabilities, P(A) ≠ 0 and P(B) ≠ 0
True
True
False
True
Now, we check the given options.
True True False True