GATE 2016 7th Feb Solution/ Key : Electrical

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

Q.7 A 3 × 3 matrix P ܲ is such that, P3 = P. Then the eigenvalues of ܲ are
(A) 1, 1, −1
(B) 1, 0.5 + j݆0.866, 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
 along a path joining the origin (0, 0, 0) and the point (1, 1, 1) is
(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
Answer: (D)

Please report if you find any errors in the questions. 
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