List of top Mathematics Questions on Application of derivatives asked in KCET

In a Mahakumbh, a drone camera is moving along $3y = x^3 - 3$. When y-coordinate changes 9 times as fast as x-coordinate, it captures good quality pictures. Then one of the precise positions of the drone at that instant is

A Youtube short video is getting viral according to $f(t) = -2t^3 + 3t^2 + 5$. At what time does the video get maximum number of shares? (t is in hours)

For the function $f(x) = x^3 - 6x^2 + 12x - 3$, $x = 2$ is:}

The value of $\sqrt{24 . 99}$ is

The point on the curve $y^2 = x$ where the tangent makes an angle of $\pi /4$ with X-axis is

The equation of the normal to the curve $y(1 + x^2) = 2 - x$ where the tangent crosses $x-axis$ is

The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 = 2$

The maximum value of $\left( \frac{1}{x} \right)^x$ is

A balloon which always remains spherical is being inflated by pumping in $10$ cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15$ cms.

A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?

The least and the greatest distances of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ are

Length of the subtangent at $ (x_1, y_1)$ on $x^n y^m = a^{m+n}, m, n > 0,$ is

For the curve $4x^5 = 5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is

A wire of length $20\,cm$ is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is ____

The set of real values of x for which $ f(x) = \frac {x}{log\, x}$ increasing, is

$P$ is the point of contact of the tangent from the origin to the curve $y = log_ex$ The length of the perpendicular drawn from the origin to the normal at $P$ is ______

A circular sector of perimeter $60$ metre with maximum area is to be constructed. The radius of the circular arc in metre must be