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Day 451: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 14 May 2026 S1

    83
    If a>4a > 4 and ∫−211x2+4x+a dx=13tan⁡−1(1)\int_{-2}^1\dfrac{1}{x^2 + 4x + a}\,dx = \dfrac{1}{3}\tan^{-1}(1), then the value of aa is

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  2. Question 2

    Determinants and Matrices. Asked once: 13 Apr 2026 S2

    64
    If A=[sec⁡θ−tan⁡θ−tan⁡θsec⁡θ],θ∈(0,π2)A = \begin{bmatrix} \sec\theta & -\tan\theta \\ -\tan\theta & \sec\theta \end{bmatrix}, \theta \in \left(0, \dfrac{\pi}{2}\right) such that A+adjA=4IA + \mathrm{adj}A = 4I, then θ=\theta =

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  3. Question 3

    Differential Equations. Asked once: 19 Apr 2025 S1

    126
    The solution of the differential equation x d2y dx2=1x\frac{{\text{ }d}^{2}y}{\text{ }dx^{2}}= 1 at x=y=1x=y= 1 with dy dx=0\frac{dy}{\text{ }dx}= 0 at x=1x= 1, is

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  4. Question 4

    Differentiation. Asked once: 14 May 2026 S1

    74
    If y=4log⁡4(x+2)−log⁡4(x−2)y = 4^{\log_4(x+2) - \log_4(x-2)}, then dydx=\dfrac{dy}{dx} =

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  5. Question 5

    Indefinite Integration. Asked once: 13 May 2026 S1

    77
    If ∫log⁡(log⁡x)4x(log⁡x)2 dx=k[1+log⁡(log⁡x)log⁡x]+c\displaystyle\int\dfrac{\log(\log x)}{4x(\log x)^2}\,dx = k\left[\dfrac{1 + \log(\log x)}{\log x}\right] + c, then the value of kk is...

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