Q.6 Consider the function ݂

*f(*z*)= z+z*∗ where z is a complex variable and z∗ denotes its complex conjugate. Which one of the following is TRUE?
(A) ݂

*f(*z*)*is both continuous and analytic
(B) ݂

*f(*z*)*is continuous but not analytic
(C) ݂

*f(*z*)*is not continuous but is analytic
(D)

*f(*z*)*is neither continuous nor analytic
Answer:

Q.7 A 3 × 3 matrix P ܲ is such that, P

^{3}= P. Then the eigenvalues of ܲ are
(A) 1, 1, −1

(B) 1, 0.5 +

*j*݆0.866, 0.5 − ݆j0.866
(C) 1,−0.5 + j݆0.866, −0.5 − ݆j0.866

(D) 0, 1, −1

Answer: (A) 1, 1, −1

Q.8 The solution of the differential
equation, for t>0,

*y"(t) + 2y'(t) + y(t) = 0*with initial
conditions

*y(0)=0,*and*y'(0)*= 1, is*u(t)*denotes the unit step function
Answer: A

Q.9 The value of the line integral

(A) 0

(B) 2

(C) 4

(D) 6

Answer: 2

Q.10 Let

*f(x)*be a real, periodic function satisfying ݂*f(-x)= -f(x).*The general form of its Fourier series representation would be