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Day 20: MHT-CET Maths

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

  1. Question 1

    Differential Equations. This type asked 7 times: 9 May 2023 S1, 13 May 2024 S2, 20 Apr 2025 S2, 13 Apr 2026 S2, 16 Apr 2026 S1, 16 Apr 2026 S2, 17 Apr 2026 S2. This one: 17 Apr 2026 S2 See all 7 of this type

    86
    The general solution of the differential equation sec⁡y+(x−esin⁡y)dydx=0\sec y + (x - e^{\sin y})\dfrac{dy}{dx} = 0 is...

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  2. Question 2

    Line and Plane. This type asked 7 times: 4 May 2023 S1, 11 May 2023 S2, 19 Apr 2025 S2, 25 Apr 2025 S2, 15 Apr 2026 S2, 16 Apr 2026 S1, 17 Apr 2026 S1. This one: 17 Apr 2026 S1 See all 7 of this type

    94
    If for some m∈Rm \in \mathbb{R} the lines L1:x+1m=y−m−1=z−11L_1 : \dfrac{x + 1}{m} = \dfrac{y - m}{-1} = \dfrac{z - 1}{1} and L2:x+2−4=y+19=z+11L_2 : \dfrac{x + 2}{-4} = \dfrac{y + 1}{9} = \dfrac{z + 1}{1} are coplanar, then line L1L_1 passes through the point

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  3. Question 3

    Line and Plane. This type asked 7 times: 3 May 2023 S2, 4 May 2023 S1, 9 May 2023 S1, 9 May 2023 S2, 14 May 2024 S1, 19 Apr 2025 S1, 15 Apr 2026 S2. This one: 15 Apr 2026 S2 See all 7 of this type

    95
    The equation of the plane passing through the point (1,2,1)(1, 2, 1) and perpendicular to the planes x+2y+2z−7=0x + 2y + 2z - 7 = 0 and 3x+3y+2z−5=03x + 3y + 2z - 5 = 0 is

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  4. Question 4

    Trigonometric Functions. This type asked 7 times: 4 May 2023 S1, 10 May 2023 S1, 10 May 2023 S2, 11 May 2023 S2, 11 May 2024 S2, 12 May 2024 S2, 11 Apr 2026 S1. This one: 11 Apr 2026 S1 See all 7 of this type

    62
    In △ABC\triangle ABC, with usual notations, if cos⁡A=12,a=3,∠B=πc6\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}, then the values of bb and cc are.....

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  5. Question 5

    Vectors. This type asked 7 times: 9 May 2023 S2, 11 May 2023 S1, 15 May 2023 S1, 16 May 2023 S1, 10 May 2024 S2, 11 May 2024 S1, 11 Apr 2026 S1. This one: 11 Apr 2026 S1 See all 7 of this type

    88
    The vector aˉ+3bˉ\bar{a} + 3\bar{b} is perpendicular to 7aˉ−5bˉ7\bar{a} - 5\bar{b} and the vector aˉ−4bˉ\bar{a} - 4\bar{b} is perpendicular to 7aˉ−2bˉ7\bar{a} - 2\bar{b}. Then the angle between aˉ\bar{a} and bˉ\bar{b} is

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