There are $9$ balls to be placed in $9$ boxes. If $5$ of the balls cannot fit into $3$ specific small boxes,find the number of ways of arranging one ball in each of the boxes.

When radiation of the wavelength $\lambda$ is incident on a metallic surface,the stopping potential is $4.8 \ V$. If the same surface is illuminated with radiation of double the wavelength,then the stopping potential becomes $1.6 \ V$. Then,the threshold wavelength for the surface is:

Which of the following metals belong to the same group in the periodic table?

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from $10 \ mg \ g ^{-1}$ and $16 \ mg \ g ^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be $4 \ mg \ g ^{-1}$ and $10 \ mg \ g ^{-1}$, respectively. At this temperature, the concentration (in $mg \ g ^{-1}$ ) of adsorbed phenol from $20 \ mg \ g ^{-1}$ aqueous solution of phenol will be $.....$ .
Use : $\log _{10} 2=0.3$

In a $\triangle ABC$,$a^2 \sin 2C + c^2 \sin 2A$ is equal to (in $\Delta$)

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to