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Day 84: MHT-CET Maths

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

  1. Question 1

    Limits. This type asked 3 times: 26 Apr 2025 S1, 15 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    62
    If f(x)=ax−35x+7f(x) = \dfrac{ax - 3}{5x + 7} and lim⁡x→0f(x)⋅lim⁡x→∞f(x)=3\lim_{x \to 0}f(x) \cdot \lim_{x \to \infty}f(x) = 3 then a=…a = \ldots

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  2. Question 2

    Vectors. This type asked 3 times: 17 Apr 2026 S2, 13 May 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    91
    If aˉ=4i^−10j^+(1−p)k^\bar{a} = 4\hat{i} - 10\hat{j} + (1 - p)\hat{k} and bˉ=12i^+(q−10)j^+3k^\bar{b} = 12\hat{i} + (q - 10)\hat{j} + 3\hat{k} satisfy aˉ×bˉ=0ˉ\bar{a} \times \bar{b} = \bar{0}, then the values of pp and qq are respectively

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  3. Question 3

    Definite Integration. This type asked 3 times: 23 Apr 2025 S1, 16 Apr 2026 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 3 of this type

    82
    If ∫01tan⁡−1[11−x+x2]dx=2k\int_0^1\tan^{-1}\left[\dfrac{1}{1 - x + x^2}\right]dx = 2k, then the value of kk is:

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  4. Question 4

    Differentiation. This type asked 3 times: 22 Apr 2025 S1, 17 Apr 2026 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 3 of this type

    71
    Let y=13x−5y = \dfrac{1}{3x - 5} and if d4ydx4=1944\dfrac{d^4y}{dx^4} = 1944, then the value of xx is

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  5. Question 5

    Line and Plane. This type asked 3 times: 19 Apr 2025 S1, 22 Apr 2025 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 3 of this type

    96
    Let aa and bb be the distances from the point (2,3,4)(2, 3, 4) to the XY plane and Y-Axis respectively. Then a2+b2=a^2 + b^2 =

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