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Day 537: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 11 May 2024 S1

    139
    In a triangle ABC, with usual notations, if m∠A=60∘m\angle A = 60^\circ, b=8b=8, a=6a=6 and B=sin⁡−1(x)B = \sin^{-1}(x), then x has the value

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  2. Question 2

    Vectors. Asked once: 14 May 2024 S1

    140
    If △ABC\triangle ABC is right angled at AA, where A=(4,2,x)A=(4,2,x), B=(3,1,8)B=(3,1,8) and C≡(2,−1,2)C\equiv(2,-1,2), then the value of xx is:

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  3. Question 3

    Indefinite Integration. Asked once: 12 May 2024 S1

    125
    The integral ∫sin⁡2xcos⁡2x(sin⁡5x+cos⁡3xsin⁡2x+sin⁡3xcos⁡2x+cos⁡5x)2dx\displaystyle\int\frac{\sin^{2}x\cos^{2}x}{(\sin^{5}x+\cos^{3}x\sin^{2}x+\sin^{3}x\cos^{2}x+\cos^{5}x)^{2}}dx is equal to

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  4. Question 4

    Line and Plane. Asked once: 15 May 2023 S1

    130
    The perpendicular distance from the origin to the plane containing the two lines x+23=y−25=z+57\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7} and x−11=y−44=z+47\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}, is

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  5. Question 5

    Trigonometric Functions. Asked once: 11 May 2024 S1

    117
    If α=3sin⁡−1611\alpha = 3\sin^{-1}\frac{6}{11} and β=3cos⁡−149\beta = 3\cos^{-1}\frac{4}{9}, where the inverse trigonometric functions take only the principal values, then the correct option is

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