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Day 27: MHT-CET Maths

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

  1. Question 1

    Line and Plane. This type asked 6 times: 4 May 2023 S2, 10 May 2024 S1, 21 Apr 2025 S2, 26 Apr 2025 S2, 15 Apr 2026 S2, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 6 of this type

    95
    A line passing through the points (1,−1,2)(1, -1, 2) and (2,0,1)(2, 0, 1) meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...

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  2. Question 2

    Line and Plane. This type asked 6 times: 2 May 2023 S1, 4 May 2023 S2, 9 May 2024 S1, 11 May 2024 S1, 16 Apr 2026 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 6 of this type

    96
    The symmetric form of the equation of the line x=ay+bx = ay + b, z=cy+dz = cy + d is

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  3. Question 3

    Probability Distribution. This type asked 6 times: 3 May 2023 S1, 10 May 2023 S1, 10 May 2024 S2, 19 Apr 2025 S2, 23 Apr 2025 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 6 of this type

    100
    Consider a game of tossing a six sided fair die. If the face that comes up is 66, the player wins Rs. 3636 and he loses Rs. k2k^2, where kk is the face that comes up k={1,2,3,4,5}k = \{1, 2, 3, 4, 5\}, then the expected winning amount in this game in Rs. is...

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  4. Question 4

    Line and Plane. This type asked 6 times: 13 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S2, 22 Apr 2025 S1, 17 Apr 2026 S1, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 6 of this type

    96
    The acute angle between the lines 2x=3y=−z2x = 3y = -z and 6x=−y=−4z6x = -y = -4z is …\ldots

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  5. Question 5

    Vectors. This type asked 6 times: 11 May 2023 S1, 9 May 2024 S1, 10 May 2024 S2, 11 May 2024 S1, 13 Apr 2026 S1, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 6 of this type

    89
    If the volume of the tetrahedron whose coterminous edges are given by the vectors aˉ=−2i^+3j^−3k^,bˉ=4i^+5j^+(λ−10)k^,cˉ=6i^+2j^−3k^\bar{a} = -2\hat{i} + 3\hat{j} - 3\hat{k}, \bar{b} = 4\hat{i} + 5\hat{j} + (\lambda - 10)\hat{k}, \bar{c} = 6\hat{i} + 2\hat{j} - 3\hat{k} is 11 cubic units, then the sum of the possible values of λ\lambda is …\ldots

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