Application of Derivatives PYQs - Last 5 Years
KCET / Mathematics / Calculus / 17 recent questions
MathematicsCalculus2022-2026
Practice 17 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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2022-2026
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Last 5 Years Application of Derivatives Questions
Showing 17 of 17 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
MCQ+1 / -02026
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)
MCQ+1 / -02026
3Application Of Derivatives
The function $f(x)=\tan x-x$
MCQ+1 / -02025
4Application Of Derivatives
If $f(x)=x e^{x(1-x)}$, then $f(x)$ is
MCQ+1 / -02024
5Application Of Derivatives
The function $x^x ; x>0$ is strictly increasing at
MCQ+1 / -02024
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
MCQ+1 / -02024
7Application Of Derivatives
For the function $f(x)=x^3-6 x^2+12 x-3$; $x=2$ is
MCQ+1 / -02024
8Application Of Derivatives
The maximum volume of the right circular cone with slant height 6 units is
MCQ+1 / -02024
9Application Of Derivatives
The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then
MCQ+1 / -02024
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
MCQ+1 / -02023
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
MCQ+1 / -02023
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
MCQ+1 / -02023
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 :
MCQ+1 / -02023
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
MCQ+1 / -02023
15Application Of Derivatives
The function \(f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100\) is strictly
MCQ+1 / -02022
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
MCQ+1 / -02022
17Application Of Derivatives
The function \(f(x)=\log (1+x)-\frac{2 x}{2+x}\) is increasing on
MCQ+1 / -02022