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Day 73: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. Asked 3 times: 10 May 2023 S1*, 10 May 2024 S2*, 19 Apr 2025 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    123
    In a game, 3 coins are tossed. A person is paid ₹150 if he gets all heads or all tails and he is supposed to pay ₹50 if he gets one head or two heads. The amount he can expect to win / lose on an average per game in ₹ is

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  2. Question 2

    Line and Plane. Asked 3 times: 4 May 2023 S1, 9 May 2023 S2, 19 Apr 2025 S1 See all 3 times it was asked

    105
    A plane passes through (1,−2,1)(1, - 2,1) and is perpendicular to the planes 2x−2y+z=02x- 2y+z= 0 and x−y+2z=4x-y+ 2z = 4. The distance of the point (1,2,2)(1,2,2) from this plane is ____\_\_\_\_ units.

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  3. Question 3

    Indefinite Integration. Asked 3 times: 15 May 2023 S2*, 9 May 2024 S1*, 14 May 2024 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    111
    If I=∫dxsin⁡(x−a)sin⁡(x−b)I = \int \frac{dx}{\sin(x-a)\sin(x-b)}, then II is given by

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  4. Question 4

    Complex Numbers. Asked 3 times: 2 May 2023 S1*, 12 May 2024 S1*, 14 May 2024 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    136
    If a>0a>0 and z=(1+i)2a−iz=\dfrac{(1+i)^2}{a-i}, i=−1i=\sqrt{-1}, has magnitude 25\dfrac{2}{\sqrt{5}}, then zz is

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  5. Question 5

    Line and Plane. Asked 3 times: 3 May 2023 S2*, 4 May 2023 S1, 14 May 2024 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    116
    Consider the lines L1:x+13=y+21=z+12L_1:\dfrac{x+1}{3}=\dfrac{y+2}{1}=\dfrac{z+1}{2} and L2:x−21=y+22=z−33L_2:\dfrac{x-2}{1}=\dfrac{y+2}{2}=\dfrac{z-3}{3}, then the unit vector perpendicular to both L1L_1 and L2L_2 is

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