EC GATE 2008 - Online Test
Q1.
Let x(t) be the input and y(t) be the output of a continuous time system.
Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4
Properties Relations
P1 : Linear but NOT time - invariant R1 : y(t) = t2x(t)
P2 : Time - invariant but NOT linear R2 : y(t) = t|x(t)|
P3 : Linear and time - invariant R3 : y(t) = |x(t)|
R4 : y(t) = x(t-5)
Answer : Option B
Explaination / Solution:
Mode function are not linear. Thus y(t) = |x(t)| is not linear but this functions is
time invariant. Option (A) and (B) may be correct.
The y(t) = t|x(t)| is not linear, thus option (B) is wrong and (a) is correct. We
can see that
R1 : y(t) = t2x(t) Linear and time variant.
R2 : y(t) = t|x(t)| Non linear and time variant.
R3 : y(t) = |x(t)| Non linear and time invariant.
R4 : y(t) = x(t-5) Linear and time invariant.
Q2. A speed signal, band limited to 4 kHz and peak voltage varying between +5 V and -5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.
Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is
Answer : Option C
Explaination / Solution:
Q3. 
The following series RLC circuit with zero conditions is excited by a unit impulse functions 𝛿(t).
For t > 0, the output voltage vc(t) is
Answer : Option D
Explaination / Solution:
Q4. { x(n)} is a real - valued periodic sequence with a period N . x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence 
is
is
Answer : Option A
Explaination / Solution:
Q5. A speed signal, band limited to 4 kHz and peak voltage varying between +5 V and -5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.
The number of quantization levels required to reduce the quantization noise by a factor of 4 wo
Answer : Option B
Explaination / Solution:
No Explaination.
Q6. 
The following series RLC circuit with zero conditions is excited by a unit impulse functions 𝛿(t).
For t > 0, the voltage across the resistor is
Answer : Option B
Explaination / Solution:
Q7. 
Group I lists a set of four transfer functions. Group II gives a list of possible step response y(t). Match the step responses with the corresponding transfer functions.
Answer : Option D
Explaination / Solution:
Q8. 
A two-port network shown below is excited by external DC source. The voltage and the current are measured with voltmeters V1,V2 and ammeters. A1,A2 (all assumed to be ideal), as indicated
Under following conditions, the readings obtained are:
The z -parameter matrix for this network is
Answer : Option C
Explaination / Solution:
From the problem statement we have
Q9. The impulse response h(t) of linear time - invariant continuous time system is given by h(t) = exp(- 2t)u(t), where u(t) denotes the unit step function.
The frequency response H(𝜔) of this system in terms of angular frequency 𝜔, is given by H(𝜔)
Answer : Option C
Explaination / Solution:
Q10.
A two-port network shown below is excited by external DC source. The voltage and the current are measured with voltmeters V1,V2 and ammeters. A1,A2 (all assumed to be ideal), as indicated
Under following conditions, the readings obtained are:
The h-parameter matrix for this network is
Answer : Option A
Explaination / Solution:
From the problem statement we have
