The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

$\sqrt{3} \operatorname{cosec} 20^{\circ} - \sec 20^{\circ}$ is equal to

If the equation $2x^2 + kxy - 6y^2 + 3x + y + 1 = 0$,$(k > 0)$ represents a pair of straight lines,then their point of intersection is

What will be the $pH$ of an aqueous solution of $1.0 \ M$ ammonium formate? (Given: $pK_{a}=3.8$ and $pK_{b}=4.8$)

The thickness of a uniform rectangular metal plate is $5 ~mm$ and the area of each surface is $5 ~cm^2$. In steady state,the temperature difference between the two surfaces of the plate is $14^{\circ} C$. If the heat flowing through the plate in one second from one surface to the other surface is $42 ~J$,then the thermal conductivity of the metal is:

If $\omega$ is a complex cube root of unity,then $225+(3 \omega+8 \omega^2)^2+(3 \omega^2+8 \omega)^2$ is equal to: