Electrical Engineering - GATE 2012 Paper Solution

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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=-1, then the value of xx is

Given

f(z)= 1z+1-2z+3. If C is a counterclockwise path in the z-plane such that z+1=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)=s2+9s+2s+1s+3s+4

is excited by sinωt. The steady-state output of the system is zero at

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

If xn=1/3n-1/2nun, 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-1310510-1810510-13

If each transmission line between the two buses is represented by an equivalent π-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: i1t=Imsinωt-Φ1, i2t=Imcosωt-Φ2.These currents are balanced if Φ1 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,

tdxdt+x=t is

The unilateral Laplace transform of f (t) is 1s2+s+1. The unilateral Laplace transform of t f (t) is

The average power delivered to an impedance (4-j3)Ω by a current 5cos100πt+100A 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

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

Consider the given circuit.

In this circuit, the race around

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