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Day 343: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 16 May 2023 S2 (same type asked 6 times) See all 6 of this type

    138
    ∫etan⁡−1x1+x2[(sec⁡−11+x2)2+cos⁡−11−x21+x2]dx\int \dfrac{e^{\tan^{-1}x}}{1+x^2}\left[\left(\sec^{-1}\sqrt{1+x^2}\right)^2 + \cos^{-1}\dfrac{1-x^2}{1+x^2}\right]dx where x>0x > 0 is

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  2. Question 2

    Complex Numbers. Asked once: 15 Apr 2026 S2 (same type asked 6 times) See all 6 of this type

    52
    If ω\omega is a complex cube root of unity, then the value of sin⁡[π(ω10+ω23)−π4]=\sin\left[\pi(\omega^{10} + \omega^{23}) - \dfrac{\pi}{4}\right] =

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  3. Question 3

    Line and Plane. Asked once: 21 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    111
    The line passing through the point (5,1,a)(5,1,a) and (3, b,1)(3,\text{ }b,1) crosses the yzyz-plane at (0,172,−132)\left( 0,\frac{17}{2},\frac{- 13}{2} \right), then the value of 2a+3b2a+ 3b is

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  4. Question 4

    Line and Plane. Asked once: 20 Apr 2025 S1 (same type asked 6 times) See all 6 of this type

    110
    The acute angle between the lines x=−2+2t,y=3−4t,z=−4+tx= - 2 + 2t,y= 3 - 4t,z = - 4 + t and x=−2−t,y=3+2t,z=−4+3tx= - 2 - t,y= 3 + 2t,z = - 4 + 3t is

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  5. Question 5

    Applications of Derivative. Asked once: 9 May 2023 S2 (same type asked 6 times) See all 6 of this type

    130
    The equation of the tangent to the curve x=acos⁡3θ,y=asin⁡3θx = a\cos^3\theta, y = a\sin^3\theta at θ=π4\theta = \frac{\pi}{4} is

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