The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3\sin^2x - 7\sin x + 2 = 0$ is

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is:

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and a linear velocity $v$ of its center of mass. It undergoes an elastic head-on collision with an identical sphere $B$ which is at rest. If there is no friction anywhere,then after the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then:

If a line makes angles $\tan ^{-1} \sqrt{7}$ and $\tan ^{-1} \frac{\sqrt{5}}{\sqrt{3}}$ with the $X$-axis and $Y$-axis respectively,then the angle made by it with the $Z$-axis is

If the transverse and conjugate axes of a hyperbola are equal,then its eccentricity is