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Applications of Definite Integral

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET 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 10 times: 3 May 2023 S1, 11 May 2023 S2, 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S1, 11 May 2024 S1, 19 Apr 2025 S2, 23 Apr 2025 S1, 11 Apr 2026 S2, 12 May 2026 S2. This one: 12 May 2026 S2 See all 10 of this type

    84
    The area of the region bounded by the parabola y2=4x−2y^2 = 4x - 2 and the line y=2x−1y = 2x - 1 is...(in sq. units)

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  2. Question 2

    This type asked 5 times: May 2021 S1, 4 May 2023 S1, 16 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    84
    The area of the region bounded by the curves y2=9xy^2 = 9x and x2=9yx^2 = 9y

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  3. Question 3

    This type asked 5 times: 10 May 2023 S1, 10 May 2024 S1, 11 Apr 2026 S1, 13 Apr 2026 S1, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 5 of this type

    85
    The area in square units of the region bounded by the curve y=16−x2y = \sqrt{16 - x^2} and lines x=0,x=4x = 0, x = 4 above the X-axis is

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  4. Question 4

    Asked 4 times: 3 May 2023 S2*, 4 May 2023 S2*, 9 May 2023 S2*, 19 May 2026 S2 (* = numbers or wording changed that year) See all 4 times it was asked

    84
    The area bounded by the curve y=x2+4,x=y,x=3,y = x^2 + 4, x = y, x = 3, and Y-axis is

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  5. Question 5

    This type asked 4 times: 22 Apr 2025 S1, 25 Apr 2025 S2, 19 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    85
    The area bounded by the parabola y=4x−x2y = 4x - x^2 and the x-axis (in sq. units) is:

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  6. Question 6

    This type asked 4 times: 17 Apr 2026 S1, 18 Apr 2026 S1, 12 May 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 4 of this type

    84
    The area of the region bounded by the line 4x+3y=124x + 3y = 12, the X-axis, and the lines x=−1x = -1 and x=2x = 2 (in sq units) is:

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  7. Question 7

    This type asked 4 times: 11 May 2023 S1, 13 Apr 2026 S2, 15 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 4 of this type

    83
    The area of the region lying in the first quadrant and bounded by the curve y=4x2y = 4x^2, the Y-axis, and the lines y=2,y=4y = 2, y = 4 is...

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  8. Question 8

    Asked 3 times: 14 May 2024 S2*, 21 Apr 2025 S2*, 15 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    83
    The area of the region bounded by the curves y=∣x−4∣,x=3y = |x - 4|, x = 3 and x=5x = 5, and the X-axis is

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  9. Question 9

    Asked 3 times: 12 May 2024 S2*, 26 Apr 2025 S1, 15 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    83
    The area of the smaller region bounded by the circle x2+y2=4x^2 + y^2 = 4 and the line x=1x = 1 is...

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  10. Question 10

    This type asked 3 times: 21 Apr 2025 S1, 19 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    86
    The area of the region bounded by the parabola y2=16xy^2 = 16x and the line x=4x = 4 is

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