If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

The total charge induced in a conducting loop when it is moved in a magnetic field depends on

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. If the angle of inclination of the plane is $60^{\circ}$,then the coefficient of friction is

$A$ particle moves along a circle of radius $\frac{20}{\pi} \; m$ with constant tangential acceleration. If the velocity of the particle is $80 \; m/s$ at the end of the second revolution after motion has begun,the tangential acceleration is:

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

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is