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Day 68: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Line and Plane. Asked 3 times: 4 May 2023 S1, 19 Apr 2025 S2*, 16 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    90
    The lines x−21=y−31=z−4−k\dfrac{x - 2}{1} = \dfrac{y - 3}{1} = \dfrac{z - 4}{-k} and x−1k=y−42=z−51\dfrac{x - 1}{k} = \dfrac{y - 4}{2} = \dfrac{z - 5}{1} are coplanar if

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  2. Question 2

    Pair of Straight Lines. Asked 3 times: 4 May 2023 S1, 19 Apr 2025 S1*, 16 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    57
    If 4ab=3h24ab = 3h^2, then the ratio of the slopes of the lines represented by ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0 is...

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  3. Question 3

    Applications of Definite Integral. 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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  4. Question 4

    Differentiation. Asked 3 times: May 2021 S1*, 26 Apr 2025 S1*, 15 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    69
    If y=tan⁡−11+sin⁡2x1−sin⁡2xy = \tan^{-1}\sqrt{\dfrac{1 + \sin 2x}{1 - \sin 2x}}, then dydx\dfrac{dy}{dx} at x=π6x = \dfrac{\pi}{6} is

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  5. Question 5

    Applications of Definite Integral. 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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