The resolving power of an astronomical telescope is $0.2\, sec$. If the central half portion of the objective lens is covered,the resolving power will be....$sec$

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

$A$ meter bridge is set up as shown to determine end corrections at $A$ and $B$. When a resistance of $15 \ \Omega$ is used in the left gap and $20 \ \Omega$ in the right gap,the null point is obtained at a distance of $42 \ cm$ from $A$. When these resistances are interchanged,the null point is obtained at a distance of $57 \ cm$ from $A$. The values of the end corrections are:

If $3 \hat{i}+3 \hat{j}+\sqrt{3} \hat{k}$, $\hat{i}+\hat{k}$, and $\sqrt{3} \hat{i}+\sqrt{3} \hat{j}+\lambda \hat{k}$ are coplanar, then $\lambda$ is equal to

$n$ moles of an ideal gas at temperature $T$ (in kelvin) occupy $V \ L$ of volume,exerting a pressure of $P$ atmospheres. What is the concentration (in $mol / L$)?

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is