Electrical Engineering - GATE 2012 Paper Solution

Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1/2 is

If $x=\sqrt{-1},$ then the value of xx is

Given

f(z)= $\frac{1}{z+1}-\frac{2}{z+3}$. If C is a counterclockwise path in the z-plane such that $\left|z+1\right|=1$, the value of $\frac1{2\pi j}\oint_cf\left(z\right)dz$ is

In the circuit shown below, the current through the inductor is

The impedance looking into nodes 1 and 2 in the given circuit is

A system with transfer function

G(s)=$\frac{\left({s}^{2}+9\right)\left(s+2\right)}{\left(s+1\right)\left(s+3\right)\left(s+4\right)}$

is excited by $\mathrm{sin}\left(\omega t\right)$. The steady-state output of the system is zero at

In the sum of products function f(X,Y,Z)=$\sum \left(2,3,4,5\right)$,the prime implicants are

If $x\left[n\right]={\left(1/3\right)}^{\left|n\right|}-{\left(1/2\right)}^{n}u\left[n\right]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be

The bus admittance matrix of a three-bus three-line system is

$Y=j\left[\begin{array}{ccc}-13& 10& 5\\ 10& -18& 10\\ 5& 10& -13\end{array}\right]$

If each transmission line between the two buses is represented by an equivalent $\mathrm{\pi }$-network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is

The slip of an induction motor normally does not depend on

A two-phase load draws the following phase currents: ${i}_{1}\left(t\right)={I}_{m}\mathrm{sin}\left(\omega t-{\Phi }_{1}\right)$, ${i}_{2}\left(t\right)={I}_{m}\mathrm{cos}\left(\omega t-{\Phi }_{2}\right)$.These currents are balanced if ${\Phi }_{1}$ is equal to

A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil (PMMC) meter connected across the same load reads

The bridge method commonly used for finding mutual inductance is

With initial condition x(1) = 0.5 , the solution of the differential equation,

$t\frac{dx}{dt}+x=t$ is

The unilateral Laplace transform of f (t) is $\frac{1}{{s}^{2}+s+1}$. The unilateral Laplace transform of t f (t) is

The average power delivered to an impedance (4-j3)$\Omega$ by a current $5\mathrm{cos}\left(100\pi t+100\right)A$ is

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

The i-v characteristics of the diode in the circuit given below are

The current in the circuit is