If $\omega$ is a complex cube root of unity,then $(x+1)(x+\omega)(x-\omega-1)$ is equal to

The same retarding force is applied to stop a train. The train stops after $80 \ m$. If the speed is doubled,then the distance will be

One mole of alkene $\underline{X}$ on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The $IUPAC$ name of $\underline{X}$ is

The first,second and third Ionisation energies ($E_1, E_2$ and $E_3$) for an element are $7 \ eV, 12.5 \ eV$ and $42.5 \ eV$ respectively. The most stable oxidation state of the element will be

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

$A$ ball moving with velocity $2 \ m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$,then their velocities (in $m/s$) after collision will be