Q3.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 BExplaination / 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
Q8.A plant transfer function is given as When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
Answer : Option AExplaination / Solution:
Given plant transfer function,
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude
Answer : Option AExplaination / Solution:
From the pole-zero plot, we obtain the transfer function as
Q10.Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let and be their complements. Which one of the following statements is FALSE?
Answer : Option CExplaination / Solution:
A and B are two independent events with probabilities, P(A) ≠ 0 and P(B) ≠ 0
Now, we check the given options.
True
True
False
True
Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0