If $$ y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^2 $$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

For the probability distribution

The expected value of X is

The value of $\int \frac{\mathrm{d} x}{7+6 x-x^2}$ is equal to

The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is equal to }\end{aligned}$