Question 1 :
Excluding stoppages, the speed of a bus is $$72\ kmph$$ and including stoppages, it is $$60\ kmph$$. For how many minutes does the bus stop per hour?

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 :
If the distance $$s$$ travelled by a particle in time $$t$$ is given by $$s=t^2-2t+5$$, then its acceleration is

Question 5 :
The position of a particle is given by $$s={ t }^{ 3 }-6{ t }^{ 2 }-15t$$ where $$s$$ in metres, $$t$$ is in seconds. If the particle is at rest, then time $$t=.....$$

Question 6 :
Consider the following statements:<br/>1. $$\dfrac {dy}{dx}$$ at a point on the curve gives slope of the tangent at that point.<br/>2. If $$a(t)$$ denotes acceleration of a particle, then $$\displaystyle \int a(t) dt + c$$ give velocity of the particle.<br/>3. If $$s(t)$$ gives displacement of a particle at time $$t$$, then $$\dfrac {ds}{dt}$$ gives its acceleration at that instant.<br/>Which of the above statements is/ are correct?

Question 7 :
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 8 :
The sides of two squares are $$x$$ and $$y$$ respectively, such that $$y = x + x^{2}$$. The rate of change of area of&#160;second square with respect to area of first square is ________.

Question 9 :
The area of an equilateral triangle of side $$'a'$$ feet is increasing at the rate of $$4 sq.ft./sec$$. The rate at which the perimeter is increasing is

Question 10 :
A stone is dropped into a quiet lake and waves move in circles at the speed of $$5$$ cm/s At the instant when the radius of the circular wave is $$8$$ cm how fast is the enclosed area increasing?<br/>

Question 11 :
The side of a square sheet is increasing at the rate&#160;of $$4 cm$$ per minute. The rate by which the area&#160;increasing when the side is $$8 cm$$ long is.

Question 12 :
What is the rate of change $$\sqrt{x^2 + 16 }$$ with respect to $$x^2$$ at x = 3 ?

Question 13 :
If the radius of a sphere is measured as $$8\ cm$$ with a error of $$0.03\ cm$$, then the approximate error calculate its volume is

Question 14 :
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 15 :
A particle moves along a straight line according to the law $$s=16-2t+3t^3$$, where $$s$$ metres is the distance of the particle from a fixed point at the end of $$t$$ second. The acceleration of the particle at the end of $$2$$ s&#160;is

Question 16 :
What is the rate of change of the area of a circle with respect to its radius $$r$$ at $$r = 6$$ $$cm$$.

Question 17 :
The interval in which the function $$x^3$$ increases less rapidly than $$6x^2+15x+15$$ is

Question 18 :
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 19 :
The interval in which the function $$f(x) = {x^3}$$ increases less rapidly than $$\,g(x) = 6{x^2} + 15x + 5$$ is :

Question 20 :
A particle moves along a curve so that its coordinates at time $$t$$ are $$\displaystyle x = t, y = \frac{1}{2} t^{2}, z =\frac{1}{3}t^{3}$$ acceleration at $$ t=1 $$ is<br>

Question 21 :
If the displacement of a particle moving in straight line is given by $$x=3t^2+2t+1$$ at time $$t$$ then&#160; the acceleration of the particle at time $$t=3$$ is

Question 22 :
If $$y = 6x -x^3$$ and $$x$$ increases at the rate of $$5$$ units per second, the rate of change of slope when $$x = 3$$ is