# Electrical Engineering - GATE 2012 Paper Solution

Question No. 1

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

Question No. 2

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

Question No. 3

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

Question No. 4

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

Question No. 5

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

Question No. 6

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

Question No. 7

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

Question No. 8

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

Question No. 9

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

Question No. 10

The slip of an induction motor normally does not depend on

Question No. 11

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

Question No. 12

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

Question No. 13

The bridge method commonly used for finding mutual inductance is

Question No. 14

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

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

Question No. 15

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

Question No. 16

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

Question No. 17

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

Question No. 18

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

The current in the circuit is