Let $u$ and $v$ be two vectors. Then,$|u-v|=||u|-|v||$ if and only if

$A$ sphere and a cube of the same material and same volume are heated up to the same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiation emitted will be

In which of the following processes,the bond order has increased and paramagnetic character has changed to diamagnetic?

$\sin ^{-1} \frac{4}{5} + 2 \tan ^{-1} \frac{1}{3}$ is equal to

$A$ small source of sound moves on a circle as shown in the figure and an observer is standing at $O$. Let $n_1, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then

If $L = 2.331 \, cm$ and $B = 2.1 \, cm$,then $L + B = $ (in $, cm$)