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

In the circuit shown in the figure,the reading of the voltmeter is $V_1$ when only $S_1$ is closed,the reading of the voltmeter is $V_2$ when only $S_2$ is closed,and the reading of the voltmeter is $V_3$ when both $S_1$ and $S_2$ are closed. Then:

If $f(x)=(\cos x)(\cos 2 x) \ldots(\cos n x)$,then $f^{\prime}(x)+\sum_{r=1}^n(r \tan r x) f(x)$ is equal to

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$, then $g^{\prime}(x)$ is equal to

In an elastic collision of two particles,which of the following quantities is conserved?

If the angle $\theta$ between the vectors $\overrightarrow{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\overrightarrow{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is such that $90^{\circ} < \theta < 180^{\circ}$, then $x$ lies in the interval