What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Given: $m = \sqrt{3} \ kg$,$\mu = \frac{1}{2\sqrt{3}}$,$\theta = 60^\circ$)

An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ km/h$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ m/s^2$):

In a meter bridge experiment,a null point is obtained at $l \text{ cm}$ from the left end. If the meter bridge wire is replaced by a wire of the same material but twice the area of cross-section,then the null point is obtained at a distance:

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

Which has the maximum number of molecules among the following?

If $|x| < \frac{1}{2}$,then the coefficient of $x^r$ in the expansion of $\frac{1+2x}{(1-2x)^2}$ is