If $A$ and $B$ are not disjoint sets,then $n(A \cup B) =$

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is

Which one of the following statements is not correct?

If a chord of the parabola $y^2=4x$ passes through its focus and makes an angle $\theta$ with the $X$-axis,then its length is

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and a radius of $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (Take $G = 6.67 \times 10^{-11} \, Nm^2/kg^2$)

The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is