$AB$ is an ionic solid. The ionic radii of $A^{+}$ and $B^{-}$ are respectively $r_c$ and $r_a$. Lattice energy of $AB$ is proportional to :

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule, the value of $\int_0^6 x^3 dx$ is approximately:

At low pressure,the van der Waals equation becomes:

$A$ block of mass $m$ is placed on a surface with a vertical cross-section given by $y = \frac{x^3}{6}$. If the coefficient of friction is $0.5$,the maximum height above the ground at which the block can be placed without slipping is

Clove oil is obtained from

The point of intersection of the line $\frac{x - 1}{3} = \frac{y + 2}{4} = \frac{z - 3}{-2}$ and the plane $2x - y + 3z - 1 = 0$ is