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

Two of the lines represented by the equation $ay^4 + bxy^3 + cx^2y^2 + dx^3y + ex^4 = 0$ will be perpendicular,then

Two bodies of masses $0.1 \,kg$ and $0.4 \,kg$ move towards each other with the velocities $1 \,m/s$ and $0.1 \,m/s$ respectively. After collision,they stick together. In $10 \,s$,the combined mass travels .......... $m$.

The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510 \ nm$ and that emitted by the North Star has the maximum value at $350 \ nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the Sun and the North Star is

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

The potential energy of a diatomic molecule is given by $U = \frac{A}{r^{12}} - \frac{B}{r^6}$,where $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is: