Question 1 :
What is the rate of change $\sqrt{x^2 + 16 }$ with respect to $x^2$ at x = 3 ?
Question 3 :
Identify the correct statements<br>(a)Every constant function is an increasing function.<br>(b)Every constant function is a decreasing function.<br>(c)Every identify function is an increasing function.<br>(d)Every identify function is a decreasing function.
Question 4 :
If the length of the diagonal of a square is increasing at the rate of 0.2 cm/sec, then rate of increase of its area when its side is $30/\sqrt{2}$ cm, is
Question 5 :
The volume of a sphere is increasing the rate of $1200\ c.cm/sec$. The rate of increase in its surface area when the radius is $10\ cm$ is
Question 6 :
If the volume of a spherical ball is increasing at the rate of $4\pi\ cc/sec$, then the rate of increase of its radius (in cm/sec), when the volume is $288\pi\ cc$, is 
Question 7 :
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 8 :
Find an angle $\theta, 0 < \theta < \dfrac{\pi}{2}$, which increases twice as fast as its sine.
Question 9 :
A point on the parabola $y^2 = 18x$ at which the ordinate increase at twice the rate of the abscissa is _______, $\left(\dfrac{dx}{dt} \neq 0\right)$.
Question 10 :
The side of a square is equal to the diameter of a circle. If the side and radius change at the same rate, then the ratio of the change of their areas is
Question 11 :
The radius of the base of a cone is increasing at the rate of $3$ cm/minute and thealtitude is decreasing at the rate of $4$ cm/minute. The rate of change of lateral surface when the radius is $7 cm$ and altitude $24 cm$ is
Question 12 :
$x$ 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 13 :
The points of the ellipse $16x^2 + 9y^2 = 400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by :
Question 14 :
If $ f(x) =\displaystyle\frac{x}{{\sin x}}$ and $g(x) =\displaystyle\frac{x}{{\tan x}}$ where $0 < x \leq1$<span class="wysiwyg-font-size-medium">then in the interval<span class="wysiwyg-font-size-medium">