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Day 422: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 15 May 2026 S2

    71
    If A−1=[10−40−12−121]=adj(A)kA^{-1} = \begin{bmatrix} 1 & 0 & -4 \\ 0 & -1 & 2 \\ -1 & 2 & 1 \end{bmatrix} = \dfrac{\mathrm{adj}(A)}{k}, then kk is a root of the equation...

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  2. Question 2

    Differential Equations. Asked once: 12 May 2026 S1

    87
    If yf(x)=g(x)+cyf(x) = g(x) + c where cc is an arbitrary constant such that dydx+yg(x)=f(x)\dfrac{dy}{dx} + yg(x) = f(x) and [f(x)]2−[g(x)]2=1[f(x)]^2 - [g(x)]^2 = 1, then ∫f(x)⋅g(x) dx=\displaystyle\int f(x) \cdot g(x)\,dx = ...

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  3. Question 3

    Differentiation. Asked once: 19 May 2026 S2

    73
    If x=1−y1+yx = \dfrac{1 - \sqrt{y}}{1 + \sqrt{y}}, then dydx=\dfrac{dy}{dx} =

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  4. Question 4

    Indefinite Integration. Asked once: 19 May 2026 S2

    79
    ∫5x12+6x11(x6+x+1)3 dx=\int \dfrac{5x^{12} + 6x^{11}}{(x^6 + x + 1)^3}\,dx =

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  5. Question 5

    Limits. Asked once: 15 May 2026 S1

    61
    lim⁡h→0log⁡e(1+2h)−2log⁡e(1+h)h2\displaystyle\lim_{h \to 0} \dfrac{\log_e(1 + 2h) - 2\log_e(1 + h)}{h^2}

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