If $\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan \mathrm{B}=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and $\tan \mathrm{C}=\sqrt{x^{-1}+x^{-2}+x^{-3}}$ then

Let X be a discrete random variable. The probability distribution of X is given below

$$ \begin{array}{|c|c|c|c|} \hline \mathrm{X} & 30 & 10 & -10 \\ \hline \mathrm{P}(\mathrm{X}) & \frac{1}{5} & \mathrm{~A} & \mathrm{~B} \\ \hline \end{array} $$

and $\mathrm{E}(\mathrm{X})=4$, then the value of AB is equal to

The projection of the line segment joining the points $(2,1,-3)$ and $(-1,0,2)$ on the line whose direction ratios are $3,2,6$ is

If $x^{\frac{2}{5}}+y^{\frac{2}{5}}=\mathrm{a}^{\frac{2}{5}}$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$