If $$\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$$ and $$\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$$, then $$\frac{\mathrm{h}^{\prime}(x)}{\mathrm{h}(x)}$$ is

The given circuit is equivalent to

A kite is $$120 \mathrm{~m}$$ high and $$130 \mathrm{~m}$$ of string is out. If the kite is moving away horizontally at the rate of $$39 \mathrm{~m} / \mathrm{sec}$$, then the rate at which the string is being out, is

$$\mathrm{ABC}$$ is a triangle in a plane with vertices $$\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)$$ and $$\mathrm{C}(\lambda, 5, \mu)$$. If median through $$\mathrm{A}$$ is equally inclined to the co-ordinate axes, then value of $$\lambda+\mu$$ is