EC GATE 2011 - Online Test
Q1. The block diagram of a system with one input it and two outputs y1 and y2 is
given below
A state space model of the above system in terms of the state vector 
and the
output vector 
is.
and the
output vector is.
Answer : Option B
Explaination / Solution:
Drawing SFG as shown below
Q2. Two systems H1(Z) and H2(Z) are connected in cascade as shown below. The
overall output y(n) is the same as the input x(n) with a one unit delay. The
transfer function of the second system H2(Z)is
Answer : Option B
Explaination / Solution:
Q3. The input-output transfer function of a plant 
The plant is
placed in a unity negative feedback configuration as shown in the figure below. 
The plant is
placed in a unity negative feedback configuration as shown in the figure below. The gain margin of the system under closed loop unity negative feedback is
Answer : Option C
Explaination / Solution:
Q4. The input-output transfer function of a plant The plant is placed in a unity negative feedback configuration as shown in the figure below.
The plant is placed in a unity negative feedback configuration as shown in the figure below. The signal flow graph that DOES NOT model the plant transfer function H(S) is
Answer : Option D
Explaination / Solution:
Q5. The solution of the differential equation 
is
is
Answer : Option C
Explaination / Solution:
lny = kx + A
Since y(0) = c thus lnc = A
lny = kx + lnc
Iny = Inekx + Inc
y = cekx
Q6. The differential equation 100 
describes a system with an
in
put x (t) and an output y(t). The system, which is initially relaxed, is excited by
a unit step input. The output y(t) can be represented by the waveform
describes a system with an
in
put x (t) and an output y(t). The system, which is initially relaxed, is excited by
a unit step input. The output y(t) can be represented by the waveform
Answer : Option A
Explaination / Solution:
100 
Applying Laplace transform we get
Roots are s = 1/10, 1/10 which lie on Right side of s plane thus unstable
Q7. The trigonometric Fourier series of an even function does not have the
Answer : Option C
Explaination / Solution:
For an even function Fourier series contains dc term and cosine term (even and odd harmonics).
Q8. The value of the integral 
where c is the circle |z| = 1 is given
by
where c is the circle |z| = 1 is given
by
Answer : Option A
Explaination / Solution:
C R Integrals is 
where C is circle |z| = 1
where C is circle |z| = 1So poles are outside the unit circle.
Q9. If 
then the initial and final values of f(t) are
respectively
then the initial and final values of f(t) are
respectively
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. A numerical solution of the equation 
can be obtained using
Newton- Raphson method. If the starting value is x = 2 for the iteration, the
value of x that is to be used in the next step is
can be obtained using
Newton- Raphson method. If the starting value is x = 2 for the iteration, the
value of x that is to be used in the next step is
Answer : Option C
Explaination / Solution:
Substituting x0 = 2 we get
Newton Raphson Method
Substituting all values we have
