Electrical Engineering - Online Test
Q1. A function 1 – x2 + x3 is defined in the closed interval [-1, 1]. The value of x , in the open interval (-1, 1) for which the mean value theorem is satisfied, is
Answer : Option B
Explaination / Solution:
Lagrange’s mean value theorem states that if a function f(x) is continuous in close interval [a, b] and differentiable in open interval (a + b), then for point c in the interval, we may define
Since, polynomial function is always continuous and differentiable, so
Q2. Which of the following is a solution to the differential equation 
Answer : Option B
Explaination / Solution:
Q3. The output F in the digital logic circuit shown in the figure is
Answer : Option A
Explaination / Solution:
In the logic circuit, the two inputs to the output AND gate are
So, we have the output
Q4.
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
Answer : Option C
Explaination / Solution:
If the two systems with impulse responseh1(t) and h2(t) are connected in cascaded configuration as shown in figure, then the overall response of the system is the convolution of the individual impulse responses.
Q5. A four-phase and an eight-phase signal constellation are shown in the figure
below.
Assuming high SNR and that all signals are equally probable, the additional
average transmitted signal energy required by the 8-PSK signal to achieve the
same error probability as the 4-PSK signal is
Answer : Option D
Explaination / Solution:
Here Pe for 4 PSK and 8 PSK is same because Pe depends on d . Since Pe is same,
d is same for 4 PSK and 8 PSK.
Additional Power SNR
Q6. Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
Answer : Option D
Explaination / Solution:
If a system is non-causal then a pole on right half of the s-plane can give BIBO stable system. But for a causal system to be BIBO all poles must lie on left half of the complex plane.
Q7. The damping ratio of a series RLC circuit can be expressed as
Answer : Option C
Explaination / Solution:
Damping ratio is given by
Q8. The probability density function (pdf) of random variable is as shown below
The corresponding commutative distribution function CDF has the form
Answer : Option A
Explaination / Solution:
No Explaination.
Q9. Consider the Boolean function, 
. Which one of the following is the complete set of essential prime implicants ?
. Which one of the following is the complete set of essential prime implicants ?
Answer : Option D
Explaination / Solution:
k -map for the Boolean function can be given as
Therefore, the simplified So P from for the Boolean function is
Q10. For a periodic signal 
the fundamental frequency in rad/s
the fundamental frequency in rad/s
Answer : Option A
Explaination / Solution:
Given, the signal
