If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is

If a bar magnet of pole strength $m$ and magnetic moment $M$ is cut equally $5$ times parallel to its axis and again $3$ times perpendicular to its axis,then the pole strength and magnetic moment of each piece are respectively

$A$ and $B$ are ideal gases. The molecular weights of $A$ and $B$ are in the ratio of $1: 4$. The pressure of a gas mixture containing equal weights of $A$ and $B$ is $P \ atm$. What is the partial pressure (in $atm$) of $B$ in the mixture?

When a spring is stretched by $2 \ cm$,it stores $100 \ J$ of energy. If it is stretched further by $2 \ cm$,the stored energy will be increased by ............. $J$.

What is formed when carbon monoxide reacts with $Cl_2$ in the presence of sunlight?

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).