The equation of the parabola with focus $(0, 0)$ and directrix $x + y = 4$ is

The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

The number of positive odd divisors of $216$ is

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

The bond dissociation energy of $B-F$ in $BF_3$ is $646 \ kJ \ mol^{-1}$ whereas that of $C-F$ in $CF_4$ is $515 \ kJ \ mol^{-1}$. The correct reason for higher $B-F$ bond dissociation energy as compared to that of $C-F$ is

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is: