If the force is given by $F = at + bt^2$,where $t$ is time,the dimensions of $a$ and $b$ are:

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

If $l, m, n$ are in arithmetic progression,then the straight line $lx + my + n = 0$ will always pass through the point:

If the equilibrium constant for the reaction $2 AB \rightleftharpoons A_2 + B_2$ is $49$,what is the equilibrium constant for $AB \rightleftharpoons \frac{1}{2} A_2 + \frac{1}{2} B_2$?

Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero,is