The minimum value of $27 \tan ^2 \theta + 3 \cot ^2 \theta$ is

The number of solutions of the system of equations $2x + y - z = 7$,$x - 3y + 2z = 1$,and $x + 4y - 3z = 5$ is:

Sunlight of intensity $1.3 ~kW ~m^{-2}$ is incident normally on a thin convex lens of focal length $20 ~cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light,in $kW m^{-2}$,at a distance $22 ~cm$ from the lens on the other side is.

At $298 \ K$,the molar conductivities at infinite dilution $(\Lambda_m^{\circ})$ of $NH_4Cl$,$KOH$,and $KCl$ are $152.8$,$272.6$,and $149.8 \ S \ cm^2 \ mol^{-1}$ respectively. The $\Lambda_m^{\circ}$ of $NH_4OH$ in $S \ cm^2 \ mol^{-1}$ and $\%$ dissociation of $0.01 \ M \ NH_4OH$ with $\Lambda_m = 25.1 \ S \ cm^2 \ mol^{-1}$ at the same temperature are:

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $p q$ is equal to

The method of concentrating the ore which makes use of the difference in density between ore and impurities is called