$A$ charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $\bar{a}+2 \bar{b}$ and $5 \bar{a}-4 \bar{b}$ are perpendicular to each other,then the angle between $\bar{a}$ and $\bar{b}$ is

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If $x = \infty$,then the value of $\mu$ is

$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out?

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and the equation having roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$ is $px^2+qx+r=0$,then $r=$

Two persons of equal height are carrying a long uniform wooden beam of length $l$. They are at distances $\frac{l}{5}$ and $\frac{l}{3}$ from the nearest ends of the rod. The ratio of the normal reaction at their heads is: