An increase in pressure required to decrease the $200\,L$ volume of a liquid by $0.004\%$ in a container is ........... $kPa$. (Bulk modulus of the liquid $= 2100\,MPa$)

If $A = \begin{bmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{bmatrix}$,find $|A|$.

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 ........ $m/s$.

The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

Amongst $LiCl$,$RbCl$,$BeCl_{2}$,and $MgCl_{2}$,the compounds with the greatest and the least ionic character,respectively,are

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$,$M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 ~ms^{-1}$ and $6 ~ms^{-1}$,respectively. The magnitude of the velocity of the heavier mass is