In an experiment with a beam balance,an unknown mass $m$ is balanced by two known masses of $16 \, kg$ and $4 \, kg$ as shown in the figure. The value of the unknown mass $m$ is ....... $kg$.

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$,$B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then,the correct order of their probabilities is

The area (in square units) of the triangle formed by the points with polar coordinates $(1, 0)$,$(2, \frac{\pi}{3})$,and $(3, \frac{2\pi}{3})$ is

Nylon-$66$ is not a ......

The excess pressure inside a spherical soap bubble of radius $1 ~cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 ~mm$ high. The surface tension of the bubble is: (in $~N/m$)

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed: