GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

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

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

Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}$. If C is a counterclockwise path in the z-plane such that |z + 1| = 1, the value of $\frac{1}{2\pi i}{\int }_{c}f(z)dz$ is

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 x${}^x$ is