A particle of mass $m$ is moving in the space under the influence a force $\overrightarrow{F}=\overrightarrow{v}\times \overrightarrow{A}$, where $\overrightarrow{v}$ is the velocity of particle and $\overrightarrow{A}$ is constant vector, given as $\overrightarrow{A}=A\hat{k}.$ At $t=0$, particle is at origin and moving with initial velocity ${\overrightarrow{v}}_0=v_1\hat{i}+v_2\hat{k}$. Choose the CORRECT statement(s).

Two skaters, $P$ and $Q$ are skating towards each other. Skater, $P$ throws a ball towards, $Q$ every $5 \mathrm{s}$ such that it always leaves her hand with speed $2 \mathrm{m} {\mathrm{s}}^{-1}$ with respect to the ground. Consider two cases: (I) $P$ runs with speed $1 \mathrm{m} {\mathrm{s}}^{-1}$ towards $Q,$ while $Q$ remains stationary. (II) $Q$ runs with speed $1 \mathrm{m} {\mathrm{s}}^{-1}$ towards $P,$ while $P$ remains stationary. Note That irrespective of speed of $P,$ ball always leaves $P$ s hand with speed $2 \mathrm{m} {\mathrm{s}}^{-1}$ with respect to the ground. Ignore gravity. Balls will be received by $Q.$

Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_A$ and $t_B$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$ vertically above $X$ and reaches $X$ in time $t_C$. Choose the correct statement.

The given graph shows the variation of velocity $\left(v\right)$ with position $\left(x\right)$ for a particle moving along a straight line

Which of the following graph shows the variation of acceleration $\left(a\right)$ with position $\left(x\right)?$

When a particle moves with variable velocity, which of the following statement are NOT correct ?
(i) Average speed = average velocity
(ii) Instantaneous speed = instantaneous velocity
(iii) Distance covered = magnitude of displacement

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Which of the following statements are correct?