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Day 83: MHT-CET Maths

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

  1. Question 1

    Complex Numbers. This type asked 3 times: 11 May 2024 S2, 23 Apr 2025 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    55
    If x=253−4ix = \dfrac{25}{3 - 4i} then 2x3−11x2+44x+27=2x^3 - 11x^2 + 44x + 27 =

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  2. Question 2

    Conic Sections. This type asked 3 times: 16 Apr 2026 S1, 17 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    60
    If the line 12x−5y+k=012x - 5y + k = 0 is tangent to the hyperbola x2−4y2=100x^2 - 4y^2 = 100, then k=k =

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  3. Question 3

    Indefinite Integration. This type asked 3 times: 13 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    80
    If ∫x3ex dx=ex(px3+qx2+rx+s)+c\displaystyle\int x^3e^x\,dx = e^x(px^3 + qx^2 + rx + s) + c, then the value of p+q+r+sp + q + r + s is

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  4. Question 4

    Indefinite Integration. This type asked 3 times: 9 May 2023 S1, 17 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    81
    ∫f(x) dx=g(x)+c\displaystyle\int f(x)\,dx = g(x) + c, then ∫xf(x2) dx=\displaystyle\int x f(x^2)\,dx =

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  5. Question 5

    Indefinite Integration. This type asked 3 times: 9 May 2023 S2, 10 May 2023 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    79
    If ∫ex−1 dx=aex−1+btan⁡−1(ex−1)+c\displaystyle\int\sqrt{e^x - 1}\,dx = a\sqrt{e^x - 1} + b\tan^{-1}(\sqrt{e^x - 1}) + c, then

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