$A$ ladder $20 \ ft$ long leans against a vertical wall. The top end slides downwards at the rate of $2 \ ft/sec$. The rate at which the lower end moves on a horizontal floor when it is $12 \ ft$ from the wall is

If the distance $s$ traveled by a particle in time $t$ is $s = a \sin t + b \cos 2t$,then the acceleration at $t = 0$ is

Coffee is draining from a conical filter,with both height and diameter equal to $15 \, cm$,into a cylindrical coffee pot with a diameter of $15 \, cm$. The rate at which coffee drains from the filter into the pot is $100 \, cm^3/min$. The rate in $cm/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \, cm$ deep,is:

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$, a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground, then:

$A$ $2 \ m$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of $25 \ cm/sec$,then the rate (in $cm/sec$) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1 \ m$ above the ground is:

If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?