Question 1 :
What is the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ $cm$.
Question 2 :
If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$, then its acceleration is
Question 3 :
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 4 :
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 is
Question 5 :
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 6 :
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 7 :
The interval in which the function $x^3$ increases less rapidly than $6x^2+15x+15$ is
Question 8 :
The side of a square sheet is increasing at the rate of $4 cm$ per minute. The rate by which the area increasing when the side is $8 cm$ long is.
Question 9 :
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 10 :
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 12 :
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 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 :
The sides of two squares are $x$ and $y$ respectively, such that $y = x + x^{2}$. The rate of change of area of second square with respect to area of first square is ________.
Question 15 :
What is the rate of change $\sqrt{x^2 + 16 }$ with respect to $x^2$ at x = 3 ?
Question 16 :
The interval in which the function $f(x) = {x^3}$ increases less rapidly than $\,g(x) = 6{x^2} + 15x + 5$ is :
Question 17 :
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 18 :
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
Question 19 :
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 20 :
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 21 :
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 22 :
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 23 :
If the rate of increase of the population of the city is $5\%$ per year. In t time population of city is P, then expression of P in terms of t is _________.
Question 24 :
A particle moves in a line with velocity given by $\dfrac{ds}{dt}=s+1$. The time taken by the particle to cover a distance of $9$ meter is
Question 25 :
A particle moves on a line according to the law $s=at^2+ bt+c$ . If the displacement after $1$ sec is $16$cm, the velocity after $2$ sec is $24$ cm/sec and acceleration is $ 8cm/sec^2$, then
Question 26 :
The volume of a ball increases at $4 \pi c.c/sec$. The rate of increases of radius when the volume is $288\pi c.c.s$ is
Question 28 :
If $\displaystyle f\left ( 0 \right )=0$ and $\displaystyle f''\left ( x \right )>0$ for all $x > 0$, then $\displaystyle \frac{f(x)}{x}$<br>
Question 29 :
A stone is dropped into a quiet lake. If the waves moves in circle at the rate of $30$ cm/sec when the radius is $50$m, the rate of increase of enclosed area is
Question 30 : <p>A particle moves in a straight line with a velocity given by $\displaystyle \frac{{dx}}{{dt}} = x + 1$  <span class="wysiwyg-font-size-medium">(x is the distance described). The time taken by a particle to traverse a distance of 99 metres is:<br/></p>
Question 31 :
If $s=ae^t+b{e}^{-t}$ is the equation of motion of a particle, then its acceleration is equal to
Question 33 :
The diameter of a circle is increasing at the rate of $1$ cm/sec. When its radius is $\pi$ , the rate of increase of its area is
Question 34 :
Two sides of a triangle are $8m$ and $5m$ in length. The angle between them is increasing at the rate of $0.08rad/s$. When the angle between the sides of fixed length is $\cfrac { \pi }{ 3 } $, the rate at which the area of the triangle is increasing, is
Question 35 :
The weight $W$ of a certain stock of fish is given by $W = nw$, where $n$ is the size of stock and $W$ is the average weight of a fish. If $n$ and $w$ change with time $t$ as $n = 2t^2 +3$ and $w= t^2 - t + 2$, then the rate of change of $W$ with respect to $t$ at $t = 1$ is
Question 36 :
If a particle moves according to the law, $s=6t^2 - \displaystyle \frac { t^3}{2}$ , then the time at which it is momentarily at rest
Question 37 :
The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius. When the radius is $1cm$ the altitude is $6 cm$. When the radius is $6cm$, then volume is increasing at the rate of $1$ Cu $cm/sec$. When the radius is $36cm$, the volume is increasing at a rate of $n$ cu. $cm/sec$. The value of '$n$' is equal to:
Question 38 :
The rate of change of area of a circle with respect to its radius at $r=2 \ cm$ is
Question 39 :
The coordinates of a moving point particle in a plane at time $t$ is given by $x=a\left( t+\sin { t } \right) $, $y=a\left( 1-\cos { t } \right) $. The magnitude of acceleration of the particle is
Question 40 :
If a particle moving along a line follows the law $s = \sqrt{1+t}$, then the accelertion is proportional to
Question 41 :
A circular metal plate is heated so that its radius increases at a rate of $0.1$ $mm/ minute$. Then the rate at which the plate's area is increasing when the radius is $50$ $cm$ is
Question 42 :
A cube of ice melts without changing its shape at the uniform rate of $4\>cm^3/min$. The rate of change of the surface area of the cube, in $cm^2/min$, when the volume of the cube is $125\>cm^3$, is
Question 43 :
A point is in motion along a hyperbola $y=\dfrac{10}{x}$ so that its abscissa x increases uniformly at rate of $1$ unit per second. Then, the rate of change of its ordinate, when the point passes through $(5, 2)$.
Question 44 :
A spherical iron ball $10 cm$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 cm^3/min$. When the thickness of ice is $5 cm$, then the rate of which the thickness of ice decreases, is.
Question 45 :
A particular point moves on the parabola $y^2=4ax $ in such a way that its projection on $y$-axis has a constant velocity. Then its projection on $x$-axis moves with
Question 46 :
If a curve passes through the point $(1, 0)$ and has slope $\left(1+\dfrac{1}{x^2}\right)$ at any point (x, y) on it, then the ordinate of point on the curve whose abscissa is $-3$, is?
Question 47 :
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 48 :
For particle moving along $x-axis$, velocity is given as a function of time as $v=2t^{2}+\sin t$. At $t=0$, particle is at origin, if the position as a function of time is $\dfrac{2t^{3}}{m}-\cos t$, then find $m$.
Question 49 :
On the curve ${x}^{3} = 12y$ , then the interval at which the abscissa changes at a faster rate than the ordinate ?<br/>
