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Day 33: MHT-CET Maths

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

  1. Question 1

    Line and Plane. This type asked 5 times: 4 May 2023 S2, 10 May 2023 S2, 16 May 2023 S2, 11 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 5 of this type

    95
    The equation of the plane containing the line x+14=y−2−1=z+53\dfrac{x + 1}{4} = \dfrac{y - 2}{-1} = \dfrac{z + 5}{3} and parallel to the vector i^+j^−k^\hat{i} + \hat{j} - \hat{k} is ax+by+cz=9ax + by + cz = 9. Then, the value of a+b−ca + b - c is:

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  2. Question 2

    Applications of Derivative. This type asked 5 times: 16 May 2023 S1, 23 Apr 2025 S1, 11 Apr 2026 S2, 14 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    77
    The coordinates of the point on the curve y=sin⁡(πx2)y = \sin\left(\dfrac{\pi x}{2}\right) at which the normal is parallel to the Y- axis are:

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  3. Question 3

    Differentiation. This type asked 5 times: 9 May 2024 S1, 12 May 2024 S1, 20 Apr 2026 S1, 15 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    74
    If f′(12)=3f'\left(\dfrac{1}{2}\right) = \sqrt{3} and g′(32)=−2g'\left(\dfrac{\sqrt{3}}{2}\right) = -2, then the derivative of f(sin⁡x)f(\sin x) with respect to g(cos⁡x)g(\cos x) at x=π6x = \dfrac{\pi}{6} is:

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  4. Question 4

    Line and Plane. This type asked 5 times: 3 May 2023 S1, 3 May 2023 S2, 12 May 2024 S2, 23 Apr 2025 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    93
    The equation of the plane containing the line rˉ=(2i^−k^)+λ(i^+j^+2k^)\bar{r} = (2\hat{i} - \hat{k}) + \lambda(\hat{i} + \hat{j} + 2\hat{k}) and perpendicular to the plane rˉ⋅(3i^−j^+k^)=20\bar{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 20 is…\ldots

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  5. Question 5

    Pair of Straight Lines. This type asked 5 times: 13 Apr 2026 S2, 15 Apr 2026 S1, 16 Apr 2026 S2, 17 Apr 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    58
    If θ1\theta_1 and θ2\theta_2 are the acute angles between the lines 3x2−7xy+4y2=03x^2 - 7xy + 4y^2 = 0 and 6x2−5xy+y2=06x^2 - 5xy + y^2 = 0 respectively, then ...

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