GATE EC 2014 Question Paper (15-Feb-2014) (Shift 2)

The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is ________.

Let X be a random variable that is uniformly chosen from the set of a positive odd number less than 100. The expectation E[x], is

For 0 ≤ t < ∞, the maximum value of the function f(t) = e${}^{-t\text{–}2e}$${}^{-2t}$ occurs at:

The value of $\underset{x\to \infty }{\lim }{\left(1+\frac{1}{x}\right)}^x$

If the characteristic equation of the differential equation $\frac{d^{2}y}{d{x}^2}+2\alpha \frac{dy}{dx}+y=0$ has two equal roots, then the values of α are