Q1.Let X be a real-valued random variable with E[X] and E[X2] denoting the
mean values of X and X2 , respectively. The relation which always holds true is
Answer : Option BExplaination / Solution: No Explaination.
The minimum eigen value of the following matrix is
Answer : Option AExplaination / Solution:
For, a given matrix [A] the eigen value is calculated as where gives the eigen values of matrix. Here, the minimum eigen value among the given options is We check the characteristic equation of matrix for this eigen value
= 3(60 - 49h- 5(25 - 14)+ 2)35 - 24h
= 33 - 55 + 22
= 0
Hence, it satisfied the characteristic equation and so, the minimum eigen value is
Q4.A polynomial with all coefficients positive has
Answer : Option DExplaination / Solution:
Given, the polynomial
Since, all the coefficients are positive so, the roots of equation is given by
f(x) = 0
It will have at least one pole in right hand plane as there will be least one sign change from (a1) to (a0) in the Routh matrix 1st column. Also, there will be a corresponding pole in left hand plane
i.e.; at least one positive root (in R.H.P)
and at least one negative root (in L.H.P)
Rest of the roots will be either on imaginary axis or in L.H.P
Q6.The differential equation 100 describes a system with an
in
put x (t) and an output y(t). The system, which is initially relaxed, is excited by
a unit step input. The output y(t) can be represented by the waveform
Answer : Option AExplaination / Solution:
100
Applying Laplace transform we get
Roots are s = 1/10, 1/10 which lie on Right side of s plane thus unstable