A boat goes from point  $A$ to $B$ downstream of a river flowing with speed  $6 \mathrm{km} {\mathrm{h}}^{-1}$ and then comes back to point $A$. If time taken in upstream journey is double of that in downstream journey then speed of boat in still water is

Graph of  $\left(\frac{1}{V}\right)$ versus $x$ for a particle under motion is shown in figure, where $v$ is velocity and $x$ is position. Find the time taken by particle to move from $x=4 \mathrm{m}$ to $x=12 \mathrm{m}$.

The motion of a particle moving along $x$-axis is represented by the equation $\frac{dv}{dt}=6-3v$, where$v$ is in $\mathrm{m} {\mathrm{s}}^{-1}$ and$t$ is in second. If the particle is at rest at$t=0$, then