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Day 416: MHT-CET Maths

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

  1. Question 1

    Circle. Asked once: 19 May 2026 S1

    62
    The equation of the director circle of the circle x2+y2+3x−8y−3=0x^2 + y^2 + 3x - 8y - 3 = 0 is:

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  2. Question 2

    Complex Numbers. Asked once: 13 May 2026 S2

    57
    If z1=3⋅e5π12iz_1 = 3 \cdot e^{\frac{5\pi}{12}i} and z2=4⋅eπ12iz_2 = 4 \cdot e^{\frac{\pi}{12}i} then z1⋅z2=⋯⋯z_1 \cdot z_2 = \cdots\cdots

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  3. Question 3

    Conic Sections. Asked once: 19 May 2026 S2

    57
    The point on the ellipse x225+y29=1\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1 which is equidistant from its foci can be

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  4. Question 4

    Definite Integration. Asked once: 19 May 2026 S2

    83
    ∫0π2(1+sin⁡x)3 dx=\int_0^{\frac{\pi}{2}}(1 + \sin x)^3\,dx =

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  5. Question 5

    Determinants and Matrices. Asked once: 19 May 2026 S1

    57
    If w=−12+i32w = -\dfrac{1}{2} + \dfrac{i\sqrt{3}}{2}, then the value of ∣1111−1−w2w21w2w4∣\begin{vmatrix} 1 & 1 & 1 \\ 1 & -1 - w^2 & w^2 \\ 1 & w^2 & w^4 \end{vmatrix} is...

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