Application of Derivatives PYQs - Last 10 Years
JEE Advanced / Mathematics / Calculus / 13 recent questions
MathematicsCalculus2017-2026
Practice 13 JEE Advanced 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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Mathematics / Calculus
2017-2026
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2022-2026
13
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2017-2026
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13PYQs
MCQ46.2%
MCQM46.2%
INTEGER7.7%
Difficulty Mix
#1 Hard7
#2 Medium6
4 in last 5 years13 in last 10 years
Last 10 Years Application of Derivatives Questions
Showing 13 of 13 filtered questions.
1Application Of Derivatives
Consider the function $f : (0, \infty) \to (-\infty, \infty)$ given by
$f(x) = \sqrt{x} \log_e(x) - x + 1$.Then which one of the following statements is TRUE?
$f(x) = \sqrt{x} \log_e(x) - x + 1$.Then which one of the following statements is TRUE?
MCQ+3 / -12026
2Application Of Derivatives
Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be defined by
$f(x) = \begin{cases} \dfrac{6x + \sin x}{2x + \sin x}, & \text{if } x \neq 0, \\ \dfrac{7}{3}, & \text{if } x = 0. \end{cases}$
Then which of the following statements is ...
$f(x) = \begin{cases} \dfrac{6x + \sin x}{2x + \sin x}, & \text{if } x \neq 0, \\ \dfrac{7}{3}, & \text{if } x = 0. \end{cases}$
Then which of the following statements is ...
MCQM+4 / -22025
3Application Of Derivatives
Let $Q$ be the cube with the set of vertices $\left\{\left(x_1, x_2, x_3\right) \in \mathbb{R}^3: x_1, x_2, x_3 \in\{0,1\}\right\}$. Let $F$ be the set of all twelve lines containing the diagonals of the six faces of the cube $Q$. Let $S$ b...
MCQ+3 / -12023
4Application Of Derivatives
Let
\(\alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)}\)
Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by
\(g(x)=2^{\alpha x}+2^{\alpha(1-x)} .\)
Then, which of the following stateme...
\(\alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)}\)
Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by
\(g(x)=2^{\alpha x}+2^{\alpha(1-x)} .\)
Then, which of the following stateme...
MCQM+4 / -22022
5Application Of Derivatives
Consider the rectangles lying the region \(\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.\) and \(\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}\)and having one side on the X-axis. The area of the rectangle whic...
MCQ+3 / -12020
6Application Of Derivatives
Let, \(f(x) = {{\sin \pi x} \over {{x^2}}}\), x > 0Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f.Then which of the following options is/ar...
MCQM+4 / -12019
7Application Of Derivatives
Let f : R \(\to\) R be given by\(f(x) = (x - 1)(x - 2)(x - 5)\). Define\(F(x) = \int\limits_0^x {f(t)dt}\), x > 0Then which of the following options is/are correct?
MCQM+4 / -12019
8Application Of Derivatives
For each positive integer n, let \({y_n} = {1 \over n}(n + 1)(n + 2)...{(n + n)^{{1 \over n}}}\). For x\(\in\)R, let [x] be the greatest integer less than or equal to x. If \(\mathop {\lim }\limits_{n \to \infty } {y_n} = L\), then the va...
INTEGER+3 / -02018
9Application Of Derivatives
If \(f(x) = \left| {\matrix{
{\cos 2x} & {\cos 2x} & {\sin 2x} \cr
{ - \cos x} & {\cos x} & { - \sin x} \cr
{\sin x} & {\sin x} & {\cos x} \cr
} } \right|\),then
MCQM+4 / -22017
10Application Of Derivatives
f : R \(\to\) R is a differentiable function such that f'(x) > 2f(x) for all x\(\in\)R, and f(0) = 1 then
MCQM+4 / -22017
11Application Of Derivatives
Which of the following options is the only CORRECT combination?
MCQ+3 / -12017
12Application Of Derivatives
Which of the following options is the only INCORRECT combination?
MCQ+3 / -12017
13Application Of Derivatives
Which of the following options is the only CORRECT combination?
MCQ+3 / -12017