What determines the nature of the path followed by a particle?

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,then answer the following question. If $v_1 \cos \theta_1 = v_2 \cos \theta_2$,then choose the incorrect statement.

$A$ particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal,the maximum height attained by it equals $4R$. The angle of projection,$\theta$,is then given by

$A$ particle moves in the $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are constants. The particle traces:

An athlete completes one round of a circular track of radius $10 \, m$ in $40 \, sec$. The distance covered by him in $2 \, min \ 20 \, sec$ is ........ $m$.

$A$ particle moves towards east with a velocity of $5\ m/s$. After $10\ s$,its direction changes towards north with the same velocity. The average acceleration of the particle is: