The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

At $T(K)$,$100 \ L$ of dry oxygen is present in a sealed container. It is subjected to silent electric discharge,till the volumes of oxygen and ozone become equal. What is the volume (in litres) of ozone formed at $T(K)$?

Data Entry - Physics

$A$ 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:

An insect crawls up a hemispherical surface very slowly (see figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by

The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is -