Differentiation PYQs - Last 5 Years
WB JEE / Mathematics / Calculus / 13 recent questions
MathematicsCalculus2021-2025
Practice 13 WB JEE Mathematics questions from Differentiation. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2021-2025
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Last 5 Years Differentiation Questions
Showing 13 of 13 filtered questions.
1Differentiation
Let $f(x)$ be a second degree polynomial. If $f(1)=f(-1)$ and $p, q, r$ are in A.P., then $f^{\prime}(p), f^{\prime}(q), f^{\prime}(r)$ are
MCQ+1 / -0.252025
2Differentiation
If ' $f$ ' is the inverse function of ' $g$ ' and $g^{\prime}(x)=\frac{1}{1+x^n}$, then the value of $f^{\prime}(x)$ is
MCQ+1 / -0.252025
3Differentiation
\(\text { If } y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log _e x}{1-6 \cdot \log _e x}\right] \text {, then } \frac{d^2 y}{d x^2}=\)
MCQ+2 / -0.52024
4Differentiation
If \(\mathrm{U}_{\mathrm{n}}(\mathrm{n}=1,2)\) denotes the \(\mathrm{n}^{\text {th }}\) derivative \((\mathrm{n}=1,2)\) of \(\mathrm{U}(x)=\frac{\mathrm{L} x+\mathrm{M}}{x^2-2 \mathrm{~B} x+\mathrm{C}}\) (L, M, B, C are constants), then $$\...
MCQ+1 / -0.252024
5Differentiation
Let \(f(x) = {x^m}\), m being a non-negative integer. The value of m so that the equality \(f'(a + b) = f'(a) + f'(b)\) is valid for all a, b > 0 is
MCQM+2 / -02023
6Differentiation
If \(x = \sin \theta\) and \(y = \sin k\theta\), then \((1 - {x^2}){y_2} - x{y_1} - \alpha y = 0\), for \(\alpha=\)
MCQ+2 / -0.52023
7Differentiation
If \(y = {\log ^n}x\), where \({\log ^n}\) means \({\log _e}{\log _e}{\log _e}\,...\) (repeated n times), then \(x\log x{\log ^2}x{\log ^3}x\,.....\,{\log ^{n - 1}}x{\log ^n}x{{dy} \over {dx}}\) is equal to
MCQ+1 / -0.252023
8Differentiation
The function \(y = {e^{kx}}\) satisfies \(\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \over {dx}} - y} \right) = y{{dy} \over {dx}}\). It is valid for
MCQ+1 / -0.252023
9Differentiation
Let \({\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}\), then \(A{y_2} + B{y_1} + Cy = 0\) is possible for, where \({y_2} = {{{d^2}y} \over {d{x^2}}},{y_1} = {{dy} \over {dx}}\)
MCQ+1 / -0.252023
10Differentiation
Suppose \(f:R \to R\) be given by \(f(x) = \left\{ \matrix{
1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr
{e^{({x^{10}} - 1)}} + {(x - 1)^2}\sin {1 \over {x - 1}},\,\mathrm{if}\,x \ne 1 \hfill \cr} \right.\)
then
then
MCQ+1 / -0.252023
11Differentiation
If \(y = {e^{{{\tan }^{ - 1}}x}}\), then
MCQ+1 / -0.252022
12Differentiation
A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of 10 m/sec. Starting from P the speed with which his shadow is run...
MCQ+1 / -0.252021
13Differentiation
Let \(g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt}\) where x > 0 and f be continuous function and f(2x) = f(x), then
MCQ+1 / -0.252021