The principal value of ${\sin ^{ - 1}}\left( { - \frac{1}{2}} \right)$ is

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$,where $[y]$ denotes the greatest integer not exceeding $y$,then $\{f(x) : |x| < 71\}$ is equal to

The two enantiomers of secondary butyl chloride differ from each other in which one of the following properties?

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is:

Lithium metal crystallises in a body-centred cubic $(BCC)$ crystal. If the length of the side of the unit cell of lithium is $351 \ pm$,the atomic radius of the lithium will be ............. $pm$.

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):