GATE EC 2015 Question Paper (01-Feb-2015) (Shift 1)

For A = ≤ft[ {*20c 1&x\\ - x&1 } ], the determinant of A${}^T$ A⁻¹ is:

The contour on the x-y plane, where the partial derivative of x² + y² with respect to y is equal to the partial derivative of 6y + 4x with respect to x is

If C is a circle of radius r with center z₀, in the complex z-plane and if n is a non-zero integer, then ${\oint }_C\frac{dz}{{\left(z-z_0\right)}^{n+1}}$ equals

Consider the function g(t) = e${}^{-t}$ sin (2πt) u(t) where u(t) is the unit step function. The area under g(t) is _________.

The value of $\sum _{n=0}^{\infty }n{\left(\frac{1}{2}\right)}^n$ is _________.