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Day 15: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. This type asked 8 times: 2 May 2023 S1, 4 May 2023 S1, 10 May 2023 S2, 16 May 2023 S2, 10 May 2024 S1, 22 Apr 2025 S2, 25 Apr 2025 S2, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 8 of this type

    67
    If tan⁡−1ax+tan⁡−13x=π4\tan^{-1}ax + \tan^{-1}3x = \dfrac{\pi}{4}, where 3ax2<13ax^2 < 1, then value of aa for x=16x = \dfrac{1}{6} is …\ldots

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  2. Question 2

    Linear Programming. This type asked 8 times: 10 May 2023 S2, 15 May 2023 S2, 9 May 2024 S2, 14 May 2024 S1, 19 Apr 2025 S1, 19 Apr 2025 S2, 23 Apr 2025 S1, 17 Apr 2026 S1. This one: 17 Apr 2026 S1 See all 8 of this type

    98
    The region satisfying the inequalities y−x≥2, x+y≤5, x≥0y - x \ge 2,\ x + y \le 5,\ x \ge 0 and y≥0y \ge 0 is

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  3. Question 3

    Differential Equations. This type asked 8 times: 4 May 2023 S1, 9 May 2023 S1, 11 May 2023 S2, 16 May 2023 S1, 14 May 2024 S2, 21 Apr 2025 S2, 25 Apr 2025 S2, 26 Apr 2025 S2. This one: 26 Apr 2025 S2 See all 8 of this type

    118
    The equation of the curve passing through the point (0,2)(0,2) given that the sum of the ordinate and abscissa of any point exceeds the slope of the tangent to the curve at that point by 5 is

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  4. Question 4

    Line and Plane. This type asked 8 times: May 2022 S1, 9 May 2023 S2, 9 May 2024 S2, 12 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S1, 21 Apr 2025 S2. This one: 21 Apr 2025 S2 See all 8 of this type

    112
    The direction ratios of the line of intersection of the planes x−y+z−5=0x-y+z- 5 = 0 and x−3y−6=0x- 3y- 6 = 0, are

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  5. Question 5

    Vectors. Asked 7 times: 3 May 2023 S1*, 16 May 2023 S1*, 12 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S2, 26 Apr 2025 S2*, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    89
    Let uˉ,vˉ,wˉ\bar{u}, \bar{v}, \bar{w} be three vectors such that ∣uˉ∣=1,∣vˉ∣=2,∣wˉ∣=3|\bar{u}| = 1, |\bar{v}| = 2, |\bar{w}| = 3. If the projection of vˉ\bar{v} along uˉ\bar{u} is equal to the projection of wˉ\bar{w} along uˉ\bar{u} and vˉ,wˉ\bar{v}, \bar{w} are perpendicular to each other, then ∣uˉ−vˉ+wˉ∣=|\bar{u} - \bar{v} + \bar{w}| =...

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