Signals and Systems - Online Test
Q1. The frequency response of a linear, time-invariant system is given by 
The step response of the system is
The step response of the system is
Answer : Option B
Explaination / Solution:
Q2. The equivalent capacitance of the input loop of the circuit shown is
Answer : Option A
Explaination / Solution:
No Explaination.
Q3. 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
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:
Q4. The RC circuit shown in the figure is
Answer : Option C
Explaination / Solution:
At ω⟶3, capacitor acts as short circuited and circuit acts as shown in fig below
At ω⟶0, 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.
Q5. Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is 
then the system response is 
If the itial state vector of the system changes to the system response becomes 
then the system response is If the itial state vector of the system changes to the system response becomes The eigenvalue and eigenvector pairs (λivi)for the system are
Answer : Option A
Explaination / Solution:
Q6. Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth
of Filter 1 be B1 and that of Filter 2 be B2. the value B1/B2 is
Answer : Option D
Explaination / Solution:
Q7.
Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is then the system response is If the itial state vector of the system changes to the system response becomes
then the system response is If the itial state vector of the system changes to the system response becomes The system matrix A is
Answer : Option D
Explaination / Solution:
No Explaination.
Q8. 
For the circuit shown in the figure, the Thevenin voltage and resistance looking into X − Y are
Answer : Option D
Explaination / Solution:
Here Vth is voltage across node also. Applying nodal analysis we get
Q9. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system ?
Answer : Option C
Explaination / Solution:
The output of causal system depends only on present and past states only.
In option (A) y(0) depends on x(- 2) and x(4).
In option (B) y(0) depends on x(1).
In option (C) y(0) depends on x(- 1).
In option (D) y(0) depends on x(5).
Thus only in option (C) the value of y(t) at t = 0 depends on x(- 1) past value.
In all other option present value depends on future value.
Q10. In the circuit shown, vC is 0 volts at t = 0 sec. For t > 0, the capacitor current iC(t), where t is in seconds is given by
Answer : Option A
Explaination / Solution:
