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Day 25: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. This type asked 6 times: 2 May 2023 S2, 4 May 2023 S2, 16 May 2023 S1, 12 May 2024 S1, 25 Apr 2025 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 6 of this type

    54
    The general solution of the equation 2sin⁡2x+sin⁡22x=22\sin^2 x + \sin^2 2x = 2 is x=(2n+1)αx = (2n + 1)\alpha or x=mπ±β,m,n∈Zx = m\pi \pm \beta, m, n \in \mathbb{Z}, then α\alpha and β\beta are the roots of the quadratic equation ______

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  2. Question 2

    Vectors. This type asked 6 times: 20 Apr 2025 S1, 20 Apr 2025 S2, 21 Apr 2025 S1, 15 Apr 2026 S1, 12 May 2026 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 6 of this type

    92
    If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  3. Question 3

    Limits. This type asked 6 times: 16 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2, 13 May 2024 S2, 14 May 2024 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 6 of this type

    63
    The value of lim⁡x→∞(x3+6x2+13−x)\lim_{x \to \infty}\left(\sqrt[3]{x^3 + 6x^2 + 1} - x\right) is:

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  4. Question 4

    Trigonometric Functions. This type asked 6 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S1, 19 Apr 2025 S1, 20 Apr 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 6 of this type

    67
    If sin⁡−1(x5)+csc⁡−1(54)=π2\sin^{-1}\left(\dfrac{x}{5}\right) + \csc^{-1}\left(\dfrac{5}{4}\right) = \dfrac{\pi}{2}, then the value of xx is

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  5. Question 5

    Vectors. This type asked 6 times: 9 May 2023 S1, 10 May 2023 S1, 11 May 2024 S2, 22 Apr 2025 S1, 15 Apr 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 6 of this type

    88
    Let u⃗\vec{u} and v⃗\vec{v} be unit vectors such that the angle between them is θ=π6\theta = \dfrac{\pi}{6}. If the adjacent sides of a parallelogram are represented by the vectors a⃗=2u⃗+3v⃗\vec{a} = 2\vec{u} + 3\vec{v} and b⃗=u⃗−v⃗\vec{b} = \vec{u} - \vec{v}, then the area of the parallelogram is

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