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Application of Integrals

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 9 times: 2021 Paper 2, 25 Jun 2022, 26 Jun 2022, 27 Jul 2022, 8 Apr 2023, 31 Jan 2024, 5 Apr 2024, 22 Jan 2025, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 9 of this type

    68
    The area of the region bounded by the curves x+3y2=0x+ 3y^{2}= 0 and x+4y2=1x+ 4y^{2}= 1 is equal to :

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  2. Question 2

    This type asked 8 times: 2021 Paper 1, 27 Jul 2022, 29 Jan 2023, 10 Apr 2023, 11 Apr 2023, 8 Apr 2024, 9 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 8 of this type

    68
    The area of the region, inside the circle (x−23)2+y2=12(x - 2\sqrt{3})^{2}+y^{2}= 12 and outside the parabola y2=23xy^{2}= 2\sqrt{3}x is

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  3. Question 3

    This type asked 5 times: 2021 Paper 17, 2021 Paper 18, 7 Apr 2025, 21 Jan 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    69
    The area of the region {(x,y):x2−8x≤y≤−x}\left\{ (x,y):x^{2}- 8x \leq y \leq - x \right\} is:

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  4. Question 4

    This type asked 5 times: 14 Jun 2022, 24 Jan 2023, 30 Jan 2024, 4 Apr 2024, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    69
    The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y):0 \leq y \leq 6 - x,\ y^{2}\geq 4x - 3,\ x \geq 0\} is :

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  5. Question 5

    This type asked 5 times: 25 Jul 2022, 27 Jan 2024, 29 Jan 2024, 28 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 5 of this type

    132
    If the area of the region {(x,y):1+x2≤y≤min⁡{x+7,11−3x}}\left\{ (x,y):1 +x^{2}\leq y \leq \min\{ x + 7,11 - 3x\} \right\} is A , then 3 A is equal to.

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  6. Question 6

    This type asked 5 times: 26 Jun 2022, 26 Jul 2022, 10 Apr 2023, 13 Apr 2023, 2 Apr 2025. This one: 2 Apr 2025 See all 5 of this type

    73
    If the area of the region {(x,y):∣4−x2∣≤y≤x2,y≤4,x≥0}\left\{ (x,y):\left| 4 - x^{2} \right| \leq y \leq x^{2},y \leq 4,x \geq 0 \right\} is (802α−β),α,β∈N\left( \frac{80\sqrt{2}}{\alpha} - \beta \right),\alpha,\beta \in N, then α+β\alpha + \beta is equal to.

  7. Question 7

    This type asked 4 times: 2021 Paper 21, 11 Apr 2023, 30 Jan 2024, 4 Apr 2025. This one: 4 Apr 2025 See all 4 of this type

    134
    A line passing through the point A(−2,0)A\left( - 2,0 \right), touches the parabola P:y2=P:y^{2}= x−2x- 2 at the point BB in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

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  8. Question 8

    This type asked 4 times: 29 Jul 2022, 29 Jan 2023, 29 Jan 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    71
    If the area of the larger portion bounded between the curves x2+y2=25x^{2}+y^{2}= 25 and y=∣x−1∣y = |x - 1| is 14(bπ+c)\frac{1}{4}(b\pi + c), b,c∈Nb,c \in N, then b+cb + c is equal to ___\_\_\_

  9. Question 9

    This type asked 4 times: 2021 Paper 5, 26 Jul 2022, 6 Apr 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    133
    If the area of the region {(x,y):−1≤x≤1,0≤y≤a+e∣x∣−e−x,a>0}\left\{ (x,y): - 1 \leq x \leq 1,0 \leq y \leq a +e^{|x|}-e^{- x},a > 0 \right\} is e2+8e+1e\frac{e^{2}+ 8e + 1}{e}, then the value of a is :

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  10. Question 10

    This type asked 4 times: 2021 Paper 3, 2021 Paper 24, 2021 Paper 26, 29 Jan 2023. This one: 29 Jan 2023 See all 4 of this type

    162
    The area of the region A={(x,y):∣cos⁡x−sin⁡x∣≤y≤sin⁡x,0≤x≤π2}A =\left\{ (x,y):|\cos x - \sin x| \leq y \leq \sin x,0 \leq x \leq\frac{\pi}{2} \right\} is

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