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Day 262: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 4 May 2023 S2 (same type asked 2 times) See all 2 of this type

    123
    If ∫4ex−252ex−5dx=Ax+Blog⁡∣2ex−5∣+c\int\frac{4e^x-25}{2e^x-5}dx = Ax+B\log|2e^x-5|+c (where c is a constant of integration) then

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  2. Question 2

    Indefinite Integration. Asked once: 11 May 2023 S2 (same type asked 2 times) See all 2 of this type

    136
    ∫2x+57−6x−x2 dx=A7−6x−x2+Bsin⁡−1(x+34)+c\int\frac{2x+5}{\sqrt{7-6x-x^2}}\,dx = A\sqrt{7-6x-x^2}+B\sin^{-1}\left(\frac{x+3}{4}\right)+c (where c is a constant of integration) then the value of A+B is

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  3. Question 3

    Circle. Asked once: 11 May 2023 S1 (same type asked 2 times) See all 2 of this type

    138
    The equation of the tangent to the circle, given by x=5cos⁡θx = 5\cos\theta, y=5sin⁡θy = 5\sin\theta at the point θ=π/3\theta = \pi/3 on it, is

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  4. Question 4

    Complex Numbers. Asked once: 10 May 2023 S2 (same type asked 2 times) See all 2 of this type

    120
    If ω=−1−i32\omega = \frac{-1-i\sqrt{3}}{2} where i=−1i = \sqrt{-1}, then the value of ∣1ωω2ωω21ω21ω∣\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix} is

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  5. Question 5

    Permutations and Combinations. Asked once: May 2021 S1 (same type asked 2 times) See all 2 of this type

    124
    The number of ways of arranging letters of the word 'HAVANA', so that V and N do not appear together, is

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