$A$ stone is dropped into a lake from a tower $500 \ m$ high. The sound of the splash will be heard by the man approximately after ..... $s$. (Take $g = 10 \ m/s^2$ and speed of sound $v = 340 \ m/s$)

The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

In the $s-t$ equation $(s=10+20t-5t^2)$,match the following columns.

Column $I$	Column $II$
$(A)$ Distance travelled in $3\,s$	$(p)$ $-20$ units
$(B)$ Displacement in $1\,s$	$(q)$ $15$ units
$(C)$ Initial acceleration	$(r)$ $25$ units
$(D)$ Velocity at $4\,s$	$(s)$ $-10$ units

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

$A$ drunkard walking in a narrow lane takes $5$ steps forward and $3$ steps backward,followed again by $5$ steps forward and $3$ steps backward,and so on. Each step is $1\; m$ long and requires $1\; s$. Plot the $x-t$ graph of his motion. How long (in $s$) does the drunkard take to fall into a pit $13\; m$ away from the start?

$A$ bead is moving in medium $1$ with a uniform speed of $1\, m/s$ for $2.5\, s$. Then it enters into air and falls freely under gravity for $2\, m$. Finally, it enters medium $2$ and immediately moves with uniform speed for $1.5\, s$. The total distance the bead has traveled is.........$m$ $(g = 10\, m/s^2)$: (in $.1$)