The sum of two numbers is $20$. If the product of the square of one number and the cube of the other is maximum,then the numbers are:

The figure shows a system of logic gates. From the study of the truth table,it can be found that to produce a high output $(1)$ at $R$,we must have

If the angles $A, B$ and $C$ of a triangle are in an arithmetic progression and if $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively,then the value of the expression $\frac{a}{c} \sin 2C + \frac{c}{a} \sin 2A$ is

$A$ body of mass $6 ~kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4}$ metres,where $t$ is time. The work done by the force in $2$ seconds is: (in $~J$)

In free space,a shell moving with velocity $60\,m/s$ along the positive $x$-axis explodes into two pieces of mass ratio $1:2$ when it passes through the origin. After the explosion,the velocity of the centre of mass is ........ $m/s$.

Which of the following is the correct increasing order of ionic character?