GATE EC 2019 Question Paper (09-Feb-2019) (Shift 1)

The value of the contour integral $\frac{1}{2\pi j}\oint {\left(z+\frac{1}{z}\right)}^{2}dz$ evaluated over the unit circle |z| = 1 is _______.

The number of distinct eigenvalues of the matrix A = ≤ft[ {*20c 2&2&3&3\\ 0&1&1&1\\ {*20c 0\\ 0 }&{*20c 0\\ 0 }&{*20c 3\\ 0 }&{*20c 3\\ 2 } } ] is equal to ______.

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = ________.

The value of the integral $\underset{0}{\overset{\pi }{\int }}\underset{y}{\overset{\pi }{\int }}\frac{\sin x}{x}dxdy,$ is equal to _______.

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by F_z≤ft( x ) = ≤ft\{ {*20c {1 - e^ - x}\\ 0 } . *20c if x ≥ 0\\ if x < 0 Then Pr(Z > 2 |Z > 1), rounded off to two decimal places, is equal to _______.