GATE EC 2014 Question Paper (16-Feb-2014) (Shift 2)

The series $\sum _{n=0}^{\infty }\frac{1}{n!}$ Converges to

The magnitude of the gradient for the function (𝑥, 𝑦, 𝑧) = 𝑥² + 3𝑦² + 𝑧³ at the point (1, 1, 1) is _________.

Let 𝑋 be a zero-mean unit variance Gaussian random variable. E[|𝑋|] is equal to _______.

If 𝑎 and 𝑏 are constants, the most general solution of the differential equation$\frac{d^{2}x}{d{t}^2}+2\frac{dx}{dt}+x=0$

The directional derivative of $f\left(x,y\right)=\frac{xy}{\sqrt{2}}\left(x+y\right)$ at (1, 1) in the direction of the unit vector at an angle of $\frac{\pi }{4}$ with y-axis, is given by ______.