Let $f(x)=e^x$,$g(x)=\sin ^{-1} x$ and $h(x)=f(g(x))$,then $\frac{h^{\prime}(x)}{h(x)}$ is equal to

Water falls from a height of $60\,m$ at the rate of $15\,kg/s$ to operate a turbine. The losses due to frictional forces are $10\%$ of energy. How much power is generated by the turbine in $kW$ $(g = 10\,m/s^2)$?

If $f_n(x) = \log \log \log \ldots \log x$ (where $\log$ is repeated $n$ times),then $\int (x f_1(x) f_2(x) \ldots f_n(x))^{-1} dx$ is equal to

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

The monomer of $[-C(CH_3)_2 - CH_2-]_n$ is ...

The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is