EC GATE 2010 - Online Test
Q1. A system with transfer function 
has an output
for the input signal 
Then, the system parameter p is
has an output for the input signal Then, the system parameter p is
Answer : Option B
Explaination / Solution:
Transfer function is given as
Amplitude Response
Alternative :
Q2. 
For the two-port network shown below, the short-circuit admittance parameter matrix is
Answer : Option A
Explaination / Solution:
Given circuit is as shown below
By writing node equation at input port
By writing node equation at output port
From (1) and (2), we have admittance matrix
Q3. 
For the asymptotic Bode magnitude plot shown below, the system transfer function can be
Answer : Option A
Explaination / Solution:
Initial slope is zero, so K = 1
At corner frequency 𝜔1 = 0.5 rad/ sec, slope increases by +20 dB/decade, so there is a zero in the transfer function at 𝜔1
At corner frequency 𝜔2 = 10 rad/ sec, slope decreases by -20 dB/decade and becomes zero, so there is a pole in transfer function at 𝜔2
Transfer function 
Q4. For parallel RLC circuit, which one of the following statements is NOT correct ?
Answer : Option D
Explaination / Solution:
A parallel RLC circuit is shown below :
Input impedance
Q5.
Two discrete time system with impulse response h1[n] = 𝛿[n - 1] and h2[n] = 𝛿[n - 2] are connected in cascade. The overall impulse response of the cascaded system is
Answer : Option C
Explaination / Solution:
Q6. The residues of a complex function 
at its poles are
at its poles are
Answer : Option C
Explaination / Solution:
Q7. 
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is
Answer : Option C
Explaination / Solution:
Impulse response of the matched filter is given by
Q8. 
In the circuit shown, the switch S is open for a long time and is closed at t = 0. The current i (t) for t ≥ 0+is
Answer : Option A
Explaination / Solution:
When the switch S is open for a long time before t < 0, the circuit is
At t = 0, inductor current does not change simultaneously, So the circuit is
Current is resistor (AB)
i(0) = 0.75/2 = 0.375 A
Similarly for steady state the circuit is as shown below
B = 0.375 - 0.5 =- 0.125
Q9. The transfer function of a discrete time LTI system is given by
Consider the following statements:
S1: The system is stable and causal for ROC: |z| > 1/2
S2: The system is stable but not causal for ROC: |z| < 1/4
S3: The system is neither stable nor causal for ROC: 1/4 < |z| < 1/2
Which one of the following statements is valid ?
Answer : Option C
Explaination / Solution:
By partial fraction H(z) can be written as
For ROC : |z| > 1/2
Thus system is causal. Since ROC of H(z) includes unit circle, so it is stable also. Hence S1 is True
For ROC : |z| < 1/4
System is not causal. ROC of H(z) does not include unity circle, so it is not stable and S3 is True
Q10. The current I in the circuit shown is
Answer : Option A
Explaination / Solution:
