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Day 527: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 19 Apr 2025 S2

    137
    ∫ x+sin⁡x1+cos⁡xdx=\int_{}^{}\ \frac{x+ \sin x}{1 + \cos x}dx=

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  2. Question 2

    Line and Plane. Asked once: 19 Apr 2025 S2

    122
    A plane passes through (2,1,2)(2,1,2) and (1,2,1)(1,2,1) and parallel to the line 2x=3y2x= 3y and z=1z= 1, then the plane also passes through the point

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  3. Question 3

    Trigonometric Functions. Asked once: 19 Apr 2025 S2

    119
    If a2+b2+c2=r2a^{2}+b^{2}+c^{2}=r^{2}, then the value of tan⁡−1(abcr)+tan⁡−1(bcar)+tan⁡−1(cabr)=\tan^{- 1}\left( \frac{ab}{cr} \right)+\tan^{- 1}\left( \frac{bc}{ar} \right)+\tan^{- 1}\left( \frac{ca}{br} \right)=

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  4. Question 4

    Vectors. Asked once: 22 Apr 2025 S1

    103
    If a‾,b‾,c‾\overline{a},\overline{b},\overline{c} are three unit vectors such that ∣a‾+b‾∣2+∣a‾+c‾∣2=8|\overline{a}+\overline{b}|^{2}+ |\overline{a}+\overline{c}|^{2}= 8, then ∣a‾+3 b‾∣2+∣a‾+3c‾∣2=|\overline{a}+ 3\overline{\text{ }b}|^{2}+ |\overline{a}+ 3\overline{c}|^{2}=

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  5. Question 5

    Applications of Derivative. Asked once: 9 May 2023 S1

    109
    Let C be a curve given by y(x)=1+4x−3y(x) = 1 + \sqrt{4x-3}, x>34x > \frac{3}{4}. If P is a point on C, such that the tangent at P has slope 23\frac{2}{3}, then a point through which the normal at P passes, is

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