The diameter of the objective of a telescope is $1 \ m$. Its resolving limit for light of wavelength $4538 \ \mathring{A}$ will be:

The vectors $\vec{AB} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and $\vec{BC} = \hat{i} - 2\hat{k}$ are the adjacent sides of a parallelogram. The angle between its diagonals is

Phenol can be converted into salicylic acid by heating with

Which of the following is true in the case of an adiabatic process,where $\gamma = C_p / C_V$?

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four particles,each of mass $m$,are gently placed on the ring at opposite points of two perpendicular diameters. The new angular velocity of the ring will be:

Hydrolysis of sucrose with dilute aqueous sulphuric acid yields