In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $C$ is equal to (in $^{\circ}$)

Identify from the following,a plant tissue in which lignin does not occur in the cell walls?

The total number of valence electrons in $4.2 \, g$ of $N_3^-$ ion is ......... $N_A$. ($N_A$ = Avogadro number)

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

$A$ healthy person eats the following diet: $5 \ gm$ raw sugar,$4 \ gm$ albumin,$10 \ gm$ pure buffalo ghee adulterated with $2 \ gm$ vegetable ghee (hydrogenated vegetable oil) and $5 \ gm$ lignin. How many calories is he likely to get?

$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is