The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term $$0, \bar{x}$$ and $$\sigma^2$$ are mean and variance of $$x_{\mathrm{i}}, \mathrm{i}=1,2, \ldots \ldots \mathrm{n}$$, then $$\sigma^2$$ is

The particular solution of differential equation $$\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3$$ is

A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is

If $$\bar{a}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ and $$\bar{b}=\hat{i}-\hat{j}-\hat{k}$$, then the projection of $$\bar{b}$$ in the direction of $$\bar{a}$$ is