EC GATE 2007 - Online Test

Q1. Three functions f(t), f2(t) and f3(t) which are zero outside the interval [0, T] are shown in the figure. Which of the following statements is correct?

Answer : Option C
Explaination / Solution:

For two orthogonal signal f (x) and g(x)

i.e. common area between f x  and g x  is zero.

Q2. The 3-dB bandwidth of the low-pass signal e-t u(t), where u(t) is the unit step function, is given by
Answer : Option A
Explaination / Solution:



Q3. An independent voltage source in series with an impedance Zs = Rs + jXs delivers a maximum average power to a load impedance ZL when
Answer : Option D
Explaination / Solution:

According to maximum Power Transform Theorem
ZLZ= (Rs - jXs)

Q4. A Hilbert transformer is a
Answer : Option A
Explaination / Solution:
No Explaination.


Q5. If the closed-loop transfer function of a control system is given as  then It is 
Answer : Option D
Explaination / Solution:

In a minimum phase system, all the poles as well as zeros are on the left half of the s −plane. In given system as there is right half zero (s = 5), the system is a non-minimum phase system.

Q6. The frequency response of a linear, time-invariant system is given by  The step response of the system is
Answer : Option B
Explaination / Solution:



Q7. A control system with PD controller is shown in the figure. If the velocity error constant KV =  000 and the damping ratio ζ = 0.5, then the value of KP and KD are

Answer : Option B
Explaination / Solution:




Q8. The z −transform X(z) of a sequence x n is given by X  It is given that the region of convergence of X(z) includes the unit circle. The value of x is
Answer : Option B
Explaination / Solution:



Q9. The transfer function of a plant is  The second-order approximation of T s using dominant pole concept is
Answer : Option D
Explaination / Solution:



Q10. The RC circuit shown in the figure is

Answer : Option C
Explaination / Solution:

At ω3, capacitor acts as short circuited and circuit acts as shown in fig below

At ω0, capacitor acts as open circuited and circuit look like as shown in fig below

So frequency response of the circuit is as shown in fig and circuit is a Band pass filter.