Differentiation PYQs - Last 5 Years
KCET / Mathematics / Calculus / 18 recent questions
MathematicsCalculus2022-2026
Practice 18 KCET Mathematics questions from Differentiation. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
18
PYQs on Page
Mathematics / Calculus
2022-2026
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Based on indexed question metadata
18
Last 5 Years
2022-2026
18
Last 10 Years
2017-2026
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18PYQs
MCQ100%
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#1 Unknown18
18 in last 5 years18 in last 10 years
Last 5 Years Differentiation Questions
Showing 18 of 18 filtered questions.
1Differentiation
If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $
MCQ+1 / -02026
2Differentiation
If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $
MCQ+1 / -02026
3Differentiation
If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $
MCQ+1 / -02026
4Differentiation
The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is
MCQ+1 / -02026
5Differentiation
The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is
MCQ+1 / -02025
6Differentiation
If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is
MCQ+1 / -02025
7Differentiation
If $y=\frac{\cos x}{1+\sin x}$, then
(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$
(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$
(c) $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$
(d) $\frac{\ma...
(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$
(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$
(c) $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$
(d) $\frac{\ma...
MCQ+1 / -02025
8Differentiation
$\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is
MCQ+1 / -02024
9Differentiation
If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is
MCQ+1 / -02024
10Differentiation
If \(f(x)\) and \(g(x)\) are two functions with \(g(x)=x-\frac{1}{x}\) and \(f \circ g(x)=x^3-\frac{1}{x^3}\), then \(f^{\prime}(x)\) is equals to
MCQ+1 / -02023
11Differentiation
If \(f(x)=1+n x+\frac{n(n-1)}{2} x^2+\frac{n(n-1)(n-2)}{6} x^3+\ldots+x^n\), then \(f^n(1)\) is equal to :
MCQ+1 / -02023
12Differentiation
If \(y=a \sin x+b \cos x\), then \(y^2+\left(\frac{d y}{d x}\right)^2\) is a
MCQ+1 / -02023
13Differentiation
If \(e^y+x y=e\) the ordered pair \(\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)\) at \(x=0\) is equal to
MCQ+1 / -02022
14Differentiation
If \(y=x^{\sin x}+(\sin x)^x\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{2}\) is
MCQ+1 / -02022
15Differentiation
If \(f(1)=1, f^{\prime}(l)=3\), then the derivative of \(f(f(f(x)))+(f(x))^2\) at \(x=1\) is
MCQ+1 / -02022
16Differentiation
If \(y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1\), then \(\frac{d^2 y}{d x^2}\) at \(x=\log _e 3\) is
MCQ+1 / -02022
17Differentiation
If \(x=e^\theta \sin \theta, y=e^\theta \cos \theta\) where \(\theta\) is a parameter, then \(\frac{d y}{d x}\) at \((1,1)\) is equal to
MCQ+1 / -02022
18Differentiation
If \(y=\left(1+x^2\right) \tan ^{-1} x-x\), then \(\frac{d y}{d x}\) is
MCQ+1 / -02022