GATE EE 2016 Question Paper (07-Feb-2016) (Shift 2)

The line integral of the vector field $F=5xz\hat{i}+\left(3x^2+2y\right)\hat{j}+x^{2}z\hat{k}$ along a path from $\left(0,0,0\right)to\left(1,1,1\right)$ parametrized by $\left(t,t^2,t\right)$ is _____.

Let P = ≤ft[ {*20c 3&1\\ 1&3 } ] consider the set $S$ of all vectors ≤ft( {*20c x\\ y } ) such that $a^2+b^2=1$ where ≤ft( {*20c a\\ b } ) = P≤ft( {*20c x\\ y } ). This $S$ is

Let the probability density function of a random variable, $X$, be given as:

$fx\left(x\right)=\frac{3}{2}{e}^{-3x}u\left(x\right)+a{e}^{4x}u\left(-x\right)$

Where $u\left(x\right)$ is the unit step function.

Then the value of 'a' and $Prob\left\{X\le 0\right\}$ respectively, are

The driving point input impedance seen from the source Vₛ of the circuit shown below, in Ω, is ______

The z-parameters of the two-port network shown in the figure are Z11 = 40 Ω, Z12 = 60 Ω, Z21 = 80 Ω and Z22 = 100 Ω. The average power delivered to R${}_L$ = 20 Ω, in watts, is _______.