Application of Derivatives PYQs - Last 10 Years

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Practice 33 KCET Mathematics questions from Application of Derivatives. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Application of Derivatives Questions

Showing 33 of 33 filtered questions.

1Application Of Derivatives

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

2Application Of Derivatives

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)

3Application Of Derivatives

The function $f(x)=\tan x-x$

4Application Of Derivatives

If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

5Application Of Derivatives

The function $x^x ; x>0$ is strictly increasing at

6Application Of Derivatives

The value of $C$ in $(0,2)$ satisfying the mean value theorem for the function $f(x)=x(x-1)^2, x \in[0,2]$ is equal to

7Application Of Derivatives

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

8Application Of Derivatives

The maximum volume of the right circular cone with slant height 6 units is

9Application Of Derivatives

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then

10Application Of Derivatives

A circular plate of radius \(5 \mathrm{~cm}\) is heated. Due to expansion, its radius increase at the rate of \(0.05 \mathrm{~cm} / \mathrm{s}\). The rate at which its area is increasing when the radius is \(5.2 \mathrm{~cm}\) is

11Application Of Derivatives

An enemy fighter jet is flying along the curve, given by \(y=x^2+2\). A soldier is placed at \((3,2)\) wants to shoot down the jet when it is nearest to him. Then, the nearest distance is

12Application Of Derivatives

A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

13Application Of Derivatives

The distance '\(s\)' in meters travelled by a particle in '\(t\)' seconds is given by \(s=\frac{2 t^3}{3}-18 t+\frac{5}{3}\). The acceleration when the particle comes to rest is :

14Application Of Derivatives

If \(u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)\) and \(v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\), then \(\frac{d u}{d v}\) is

15Application Of Derivatives

The function \(f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100\) is strictly

16Application Of Derivatives

The coordinates of the point on the \(\sqrt{x}+\sqrt{y}=6\) at which the tangent is equally inclined to the axes is

17Application Of Derivatives

The function \(f(x)=\log (1+x)-\frac{2 x}{2+x}\) is increasing on

18Application Of Derivatives

The function \(f(x)=x^2-2 x\) is strictly decreasing in the interval

19Application Of Derivatives

The cost and revenue functions of a product are given by \(c(x)=20 x+4000\) and \(R(x)=60 x+2000\) respectively, where \(\mathrm{x}\) is the number of items produced and sold. The value of \(x\) to earn profit is

20Application Of Derivatives

A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of \(t=4\) is \(k\), then the value of \(5 k\) is

21Application Of Derivatives

The maximum slope of the curve \(y=-x^3+3 x^2+2 x-27\) is

22Application Of Derivatives

If the curves \(2 x=y^2\) and \(2 x y=K\) intersect perpendicularly, then the value of \(K^2\) is

23Application Of Derivatives

The maximum value of \(\frac{\log _e x}{x}\), if \(x>0\) is

24Application Of Derivatives

If the side of a cube is increased by \(5 \%\), then the surface area of a cube is increased by

25Application Of Derivatives

The interval in which the function \(f(x)=x^3-6 x^2+9 x+10\) is increasing in

26Application Of Derivatives

The sides of an equilateral triangle are increasing at the rate of \(4 \mathrm{~cm} / \mathrm{sec}\). The rate at which its area is increasing, when the side is \(14 \mathrm{~cm}\)

27Application Of Derivatives

$f(x)=x^x$ has stationary point at

28Application Of Derivatives

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

29Application Of Derivatives

Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $3 \%$ is

30Application Of Derivatives

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

31Application Of Derivatives

The function $f(x)=x^2+2 x-5$ is strictly increasing in the interval

32Application Of Derivatives

The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is

33Application Of Derivatives

The value of $c$ in mean value theorem for the function $f(x)=x^2$ in $[2,4]$ is