If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$, then the value of $\mathrm{P}_1 \mathrm{P}_2$ is

$$\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=$$

The cumulative distribution function of a discrete random variable X is given by

Then $\mathrm{E(X^2)=}$

A five digit number divisible by 3 is to be formed using the digits $0,1,2,3,4,5$ without repetition, then the total number of ways this can be done is