Consider three observations $\mathrm{a}, \mathrm{b}$ and c such that $b=a+c$. If the standard deviation of $\mathrm{a}+2, \mathrm{~b}+2, \mathrm{c}+2$ is d , then ............ holds.

The area (in sq. units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0, X$-axis and lying in the first quadrant is

If the lengths of the sides of triangle are 3,5,7, then the largest angle of the triangle is

If $\mathrm{f}(x)=\sin ^{-1}\left(\frac{2 \cdot 3^x}{1+9^x}\right)$, then $\mathrm{f}^{\prime}\left(\frac{1}{2}\right)$ equals