Question 1 :
If the displacement of a particle moving in straight line is given by $x=3t^2+2t+1$ at time $t$ then  the acceleration of the particle at time $t=3$ is
Question 2 :
A ladder, 5 meter long, standing on a horizontal floor, leans against vertical wall. If the top of the ladder slides downwards at the rate of 10cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is:
Question 3 :
The radius of a circular plate is increased at $ 0.01 \text {cm/sec}.$ If the area is increased at the rate of $\frac{\pi }{{10}}$. Then its radius is 
Question 4 :
The rate of change of surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2 cm/sec$ is proportional to
Question 5 :
The radius of a circle is uniformly increasing at the rate of $3cm/s$. What is the rate of increase in area, when the radius is $10cm$?
Question 6 :
The displacement of a body varies with the time as $S=t^{3}+3t^{2}+2t-1$. If the velocity at $t=4\ sec$ is $2+12\ Km/s$, then find $k$
Question 7 :
A balloon which always remain spherical has a variable diameter $\cfrac { 3 }{ 2 } \left( 2x+3 \right) $. The rate of change of its volume w.r.t $x$, is
Question 8 :
The distance moved by the particular in time $t$ is given by $s = t^{3} - 12t^{2} + 6t + 8$. At the instant, when its acceleration is zero the velocity is
Question 9 :
Find the rate of change of the area of a circle with respect to its radius $r$ when<br>(i) $r = 3$ cm<br>(ii) $r=4$ cm
Question 10 :
Water is flowing into cylindrical tank of radius $7\ ft$ at the rate of $22\ c.ft/sec$. Then the rate of change in the water level is
Question 11 :
$x$ and $y$ are the sides of two squares such that $y=x-x^{2}$. The rate of change of the area of the second square with respect to that of the first square is
Question 12 :
The radius of a sphere is changing at the rate of $0.1{ cm }/{ s }$. The rate of change of its surface area when the radius is $200 cm$, is
Question 13 :
On the curve ${x}^{3} = 12y$ , then the interval at which the abscissa changes at a faster rate than the ordinate ?<br/>
Question 14 :
The rate at which ice-ball melts is proportional to the amount of ice in it. If half of it melts in $20$ minutes, the amount of ice left after $40$ minutes compared to it original amount is
Question 15 :
A particle moving on a curve has the position given by $\displaystyle x=f'(t)\sin t+f''(t)\cos t,y=f'(t)\cos t-f''(t)\sin t$ at time $t$ where $f$ is a thrice-differentiable function.Then the velocity of the particle at time $t$ is
