In $NaCl$ the centres of two nearest like-charged ions are present at a distance of

The maximum value of $xy$ when $x + 2y = 8$ is

Passage cells are thin-walled cells found in

$A$ lead bullet at $27\,^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

$ABC$ is a triangular plate of uniform thickness. Its sides are in the ratio as shown in the figure. Let $I_{AB}$,$I_{BC}$,and $I_{CA}$ be the moments of inertia of the plate about the sides $AB$,$BC$,and $CA$ respectively. Which of the following relations is true for this arrangement?

At $25^{\circ}C$,the solubility product of $Mg(OH)_2$ is $1.0 \times 10^{-11}$. At what $pH$ value will the precipitation of $Mg^{2+}$ ions begin in a solution containing $0.001 \ M \ Mg^{2+}$ ions?