$A$ beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20 \; Vm^{-1}$ and $0.5 \; T$ at right angles to the direction of motion of the electrons. What is the velocity (in $m/s$) of the electrons?

If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin to a plane,then the equation of that plane is

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be

The equation of the common tangent to the circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ is

The value of $\lim_{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ is

In a compound microscope,the focal lengths of the objective and the eye lens are $2.5 \, cm$ and $5 \, cm$ respectively. An object is placed at $3.75 \, cm$ before the objective and the image is formed at the least distance of distinct vision. Then,the distance between the two lenses (i.e.,the length of the microscope tube) will be......$cm$.