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Day 459: MHT-CET Maths

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

  1. Question 1

    Complex Numbers. Asked once: 9 May 2024 S2

    132
    If Z1=2+iZ_1 = 2+i and Z2=3−4iZ_2 = 3-4i and Z1‾Z2‾=a+bi\dfrac{\overline{Z_1}}{\overline{Z_2}} = a+bi, then the value of −7a+b-7a + b is (where i=−1i = \sqrt{-1} and a,b∈Ra,b \in \mathbb{R})

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  2. Question 2

    Conic Sections. Asked once: 18 Apr 2026 S1

    58
    If the eccentricity of the ellipse x2a2+y2b2=1,(a>b)\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1, (a > b) is 23\dfrac{2}{3} and its focal chord is 3x+2y−6=03x + 2y - 6 = 0, then the value of a2+b2a^2 + b^2 is...

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  3. Question 3

    Definite Integration. Asked once: 13 May 2026 S2

    83
    If ∫0∞1(x2+1)(x2+16) dx=πk2−9\int_0^\infty\dfrac{1}{(x^2 + 1)(x^2 + 16)}\,dx = \dfrac{\pi}{k^2 - 9}, then k=…k = \ldots

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  4. Question 4

    Determinants and Matrices. Asked once: 11 Apr 2026 S1

    63
    If A=12[−1−33−1]A = \dfrac{1}{2}\begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix} then A−1−A2A^{-1} - A^2 is not

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  5. Question 5

    Differentiation. Asked once: 13 May 2026 S1

    71
    If f(x)=22x−1f(x) = 2^{2x-1} and ϕ(x)=−2x+xlog⁡4\phi(x) = -2^x + x\log 4, such that f′(x)>ϕ′(x)f'(x) > \phi'(x), then the set of all possible values of xx is...

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