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Objective Type Set
Online MCQ Assignment
Question Solution
Solved Question

1. Which of the following signals are monotonic in nature?
a) 1-exp(-t)
b) 1-exp(sin(t))
c) log(tan(t))
d) cos(t)

View Answer

Answer: a [Reason:] All of the other functions have a periodic element in them, which means the function attains the same value after a period of time, which should not occur for a monotonic function.

2. What is the period of the following signal, x(t) = sin(18*pi*t + 78 deg)?
a) 19
b) 29
c) 13
d) 49

View Answer

Answer: b [Reason:] The signal can be expressed as sin(wt + d), where the time period = 2*pi/w.

3. Which of the following signals is monotonic?
a) x(t) = t3 – 2t
b) x(t) = sin(t)
c) x(t) = sin22(t) + cos22(t) – 2t
d) x(t) = log(cos(t))

View Answer

Answer: c [Reason:] c) reduces to 1 – 2t, which is a strictly decreasing function.

4. For the signal, x(t) = log(cos(a*pi*t+d)) for a = 50 Hz, what is the time period of the signal, if periodic?
a) 0.16s
b) 0.08s
c) 0.12s
d) 0.04s

View Answer

Answer: d [Reason:] Time period = 2*pi/(50)pi = 1/25 = 0.04s

5. What are the steady state values of the signals, 1-exp(-t), and 1-k*exp(-k*t)?
a) 1, k
b) 1, 1/k
c) k, k
d) 1, 1

View Answer

Answer: d [Reason:] Consider limit at t tending to infinity, we obtain 1 for both cases.

6. For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?
a) Yes
b) Never
c) Not always
d) None of the mentioned

View Answer

Answer: c [Reason:] If the bounded function, is say y = 2, then the integral ceases to hold. Similarly, if it is just the block square function, it is finite. Hence, it depends upon the spread of the signal on either side. If the spread is finite, the integral will be finite.

7. For the signal x(t) = a – b*exp(-ct), what is the steady state value, and the initial value?
a) c, b
b) c, c-a
c) a, a-b
d) b, a-b

View Answer

Answer: c [Reason:] Put the limits as t tends to infinity and as t tends to zero.

8. For a double sided function, which is odd, what will be the integral of the function from -infinity to +infinity equal to?
a) Non-zero Finite
b) Zero
c) Infinite
d) None of the mentioned

View Answer

Answer: b [Reason:] For an odd function, f(-x) = -f(x), thus the integrals will cancel each other, giving zero.

9. Find where the signal x(t) = 1/(t2 – 3t + 2) finds its maximum value between (1.25, 1.75):
a) 1.40
b) 1.45
c) 1.55
d) 1.50

View Answer

Answer: d [Reason:] Differentiate the function for an optima, put it to zero, we will obtain t = 1.5 as the required instant.

10. Is the signal x(t) = exp(-t)*sin(t) periodic in nature?
a) Yes
b) No

View Answer

Answer: b [Reason:] Though sin(t) is a periodic function, exp(-t) is not a periodic function, thus leading to non-periodicity.

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