Application of Integration PYQs - Last 5 Years
JEE Advanced / Mathematics / Calculus / 7 recent questions
MathematicsCalculus2022-2026
Practice 7 JEE Advanced Mathematics questions from Application of Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
7
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Mathematics / Calculus
2022-2026
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7
Last 5 Years
2022-2026
7
Last 10 Years
2017-2026
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Question Types
7PYQs
INTEGER71.4%
MCQ28.6%
Difficulty Mix
#1 Hard4
#2 Medium3
7 in last 5 years7 in last 10 years
Last 5 Years Application of Integration Questions
Showing 7 of 7 filtered questions.
1Application Of Integration
Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .
INTEGER+2 / -02026
2Application Of Integration
Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...
INTEGER+2 / -02026
3Application Of Integration
Let ℝ denote the set of all real numbers. Then the area of the region
$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x}, 5x - 4y - 1 > 0, 4x + 4y - 17 < 0 \right\} $
is
$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x}, 5x - 4y - 1 > 0, 4x + 4y - 17 < 0 \right\} $
is
MCQ+3 / -12025
4Application Of Integration
Let the function $f:[1, \infty) \rightarrow \mathbb{R}$ be defined by
$$ f(t)=\left\{\begin{array}{cc} (-1)^{n+1} 2, & \text { if } t=2 n-1, n \in \mathbb{N}, \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2...
$$ f(t)=\left\{\begin{array}{cc} (-1)^{n+1} 2, & \text { if } t=2 n-1, n \in \mathbb{N}, \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2...
INTEGER+4 / -02024
5Application Of Integration
Let $S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.$ and $\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal ...
MCQ+3 / -12024
6Application Of Integration
Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow \mathbb{R}$ be the function defined by
$$
f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{...
$$
f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{...
INTEGER+4 / -02023
7Application Of Integration
Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by
$$
f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}
$...
$$
f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}
$...
INTEGER+3 / -12022