Which of the following is an example of a new crop?

Two particles $A$ and $B$ move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment,their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for their collision is

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on:

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals

The centre of mass of three particles of masses $1 ~kg, 2 ~kg$ and $3 ~kg$ is at $(2,2,2)$. The position of the fourth mass of $4 ~kg$ to be placed in the system so that the new centre of mass is at $(0,0,0)$ is:

Which one of the following compounds gives aspirin on reacting with acetic anhydride in the presence of conc. $H_2SO_4$?