The equivalent mass of an element is $4$. Its chloride has a vapor density of $59.25$. What is the valency of the element?

The effect due to a uniform magnetic field on a freely suspended magnetic needle is as follows:

The surface of a metal is illuminated with light of $400\, nm$. The maximum kinetic energy of the ejected photoelectrons was found to be $1.68\, eV$. The work function of the metal is.......$eV$ $(hc = 1240\, eV\, nm)$.

Acidified potassium permanganate solution is decolourised by

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\,mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-