When a body moves in a circular path,no work is done by the force since,

$A$ ball of mass $160\, g$ is thrown up at an angle of $60^\circ$ to the horizontal at a speed of $10\, m\,s^{-1}$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly ........ $kg\, m^2/s$ $(g = 10\, m\,s^{-2})$.

The number of roots of the equation $(81)^{\sin ^2 x} + (81)^{\cos ^2 x} = 30$ in the interval $[0, \pi]$ is equal to

Match the following and choose the correct answer:-
$(A)$ Implantation $(i)$ Vagina
$(B)$ Capacitation (ii) Ovary
$(C)$ Folliculogenesis (iii) Uterus
$(D)$ Fertilisation (iv) Fallopian tube

$\int \frac{\cos ^3 x+\cos ^5 x}{\sin ^2 x+\sin ^4 x} d x=$

The points in the set $\{z \in \mathbb{C} : \arg \left(\frac{z-2}{z-6i}\right) = \frac{\pi}{2}\}$ (where $\mathbb{C}$ denotes the set of all complex numbers) lie on the curve which is a