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Day 6: MHT-CET Maths

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

  1. Question 1

    Differentiation. This type asked 10 times: May 2022 S1, 2 May 2023 S2, 3 May 2023 S1, 10 May 2023 S2, 16 May 2023 S1, 21 Apr 2025 S2, 13 Apr 2026 S2, 19 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 10 of this type

    73
    If y=sin⁡(2sin⁡−1x)y = \sin(2\sin^{-1}x), then dydx=\dfrac{dy}{dx} = ______

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  2. Question 2

    Line and Plane. This type asked 10 times: 2 May 2023 S1, 3 May 2023 S1, 9 May 2023 S1, 9 May 2023 S2, 10 May 2023 S1, 10 May 2024 S1, 22 Apr 2025 S1, 25 Apr 2025 S2, 12 May 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 10 of this type

    93
    Let the line x−23=y−1−5=z+22\dfrac{x - 2}{3} = \dfrac{y - 1}{-5} = \dfrac{z + 2}{2} lie in the plane x+3y−αz+β=0x + 3y - \alpha z + \beta = 0. Then (α,β)(\alpha, \beta) equals

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  3. Question 3

    Linear Programming. This type asked 10 times: May 2022 S1, 4 May 2023 S2, 9 May 2023 S2, 16 May 2023 S1, 11 May 2024 S2, 12 May 2024 S2, 25 Apr 2025 S2, 18 Apr 2026 S1, 18 Apr 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 10 of this type

    97
    The maximum value of Z=7x−6yZ = 7x - 6y subject to 0≤x≤50 \le x \le 5 and 0≤y≤30 \le y \le 3 is...

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  4. Question 4

    Applications of Definite Integral. 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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  5. Question 5

    Limits. This type asked 10 times: May 2022 S1, 4 May 2023 S1, 10 May 2023 S1, 15 May 2023 S2, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S1, 13 May 2024 S2, 22 Apr 2025 S1, 12 May 2026 S1. This one: 12 May 2026 S1 See all 10 of this type

    70
    If the function defined by f(x)={ax2+bx+1,∣2x−3∣≥23x+2,12<x<52f(x) = \begin{cases} ax^2 + bx + 1, & |2x - 3| \ge 2 \\ 3x + 2, & \dfrac{1}{2} < x < \dfrac{5}{2} \end{cases} is continuous in its domain, then the values of aa and bb respectively are

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