$A$ charged particle moves through a magnetic field in a direction perpendicular to it. Then the

From a uniform wire,two circular loops are made: $(i)$ $P$ of radius $r$ and $(ii)$ $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).

The quantum number which explains the line spectra observed as doublets in the case of hydrogen and alkali metals and doublets and triplets in the case of alkaline earth metals is

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is

All of the following substances react with water. Which pair among them will produce the same gaseous product upon reaction with water?

$A$ uniform chain of length $2\, m$ is kept on a table such that a length of $60\, cm$ hangs freely from the edge of the table. The total mass of the chain is $4\, kg$. What is the work done in pulling the entire chain on the table? ................ $J$