The number of electrons in the valence shell of the central atom of a molecule is $8$. The molecule is

The line $2x + \sqrt{6}y = 2$ is a tangent to the curve $x^2 - 2y^2 = 4$. The point of contact is

$A$ point source of light is placed $4 \, m$ below the surface of water of refractive index $5/3$. The minimum diameter of a disc that should be placed over the source on the surface of water to cut off all light coming out of the water is ...... $m$.

Two polaroids are placed in the path of an unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarization axis makes an angle $\theta$ with the polarization axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be:

What is the output $Y$ in the following circuit,when all the three inputs $A, B, C$ are first $0$ and then $1$?

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is