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 x^{x} 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, C_{1} and C_{2} are ideal capacitors. C_{1} 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