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Day 534: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 2 May 2023 S1

    137
    If y=asin⁡x+bcos⁡xy = a\sin x + b\cos x (where aa and bb are constants), then y2+(dydx)2y^2 + \left(\dfrac{dy}{dx}\right)^2 is

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  2. Question 2

    Indefinite Integration. Asked once: 12 May 2024 S2

    125
    ∫(tan⁡(1x)x)2dx=\int \left(\dfrac{\tan\left(\frac{1}{x}\right)}{x}\right)^{2}dx =

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  3. Question 3

    Line and Plane. Asked once: 16 May 2023 S2

    133
    A plane makes positive intercepts of unit length on each of X and Y axis. If it passes through the point (−1,1,2)(-1,1,2) and makes angle θ\theta with the X-axis, then θ\theta is

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  4. Question 4

    Trigonometric Functions. Asked once: 11 May 2024 S2

    117
    In triangle ABC with usual notations b=3b=\sqrt{3}, c=1c=1, ∠A=30∘\angle A=30^{\circ}, then the largest angle of the triangle is

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  5. Question 5

    Vectors. Asked once: 19 Apr 2025 S2

    104
    Let OA‾=a‾,OB‾=b‾\overline{OA}=\overline{a},\overline{OB}=\overline{b} and if the vector along the angle bisector of ∠AOB\angle AOB is given by xa‾∣a‾∣+y b‾∣ b‾∣x\frac{\overline{a}}{|\overline{a}|}+y\frac{\overline{\text{ }b}}{|\overline{\text{ }b}|} then

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