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Day 51: MHT-CET Maths

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

  1. Question 1

    Differentiation. This type asked 4 times: 9 May 2023 S1, 9 May 2023 S2, 25 Apr 2025 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    69
    If y=tan⁡−1(2x5/21−x5)y = \tan^{-1}\left(\dfrac{2x^{5/2}}{1 - x^5}\right), then dydx\dfrac{dy}{dx} is equal to ....

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  2. Question 2

    Mathematical Logic. This type asked 4 times: 11 Apr 2026 S1, 11 Apr 2026 S2, 17 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    67
    Let A={1,2,3,…,10}A = \{1, 2, 3, \ldots, 10\}. Consider the following statements: p:∀x∈A, x2−x>0p : \forall x \in A,\ x^2 - x > 0 q:∃x∈Aq : \exists x \in A, such that x+10=20x + 10 = 20 Then the truth values of pp and qq are respectively ____

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  3. Question 3

    Trigonometric Functions. This type asked 4 times: 21 Apr 2025 S2, 22 Apr 2025 S1, 20 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    70
    If x∈[0,1)x \in [0, 1) then the value of tan⁡{12sin⁡−1(2x1+x2)+12cos⁡−1(1−x21+x2)}\tan\left\{\dfrac{1}{2}\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) + \dfrac{1}{2}\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right)\right\} is:

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  4. Question 4

    Trigonometric Functions. This type asked 4 times: 11 May 2023 S1, 25 Apr 2025 S2, 20 Apr 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 4 of this type

    52
    If α\alpha and β\beta are the solutions of 2cos⁡θ=12\cos\theta = 1 in the interval [0,2π)[0, 2\pi), then the solutions of 2cos⁡θ+cos⁡(α+β)=02\cos\theta + \cos(\alpha + \beta) = 0 in the interval [0,2π)[0, 2\pi) are...

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  5. Question 5

    Applications of Definite Integral. 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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