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Day 427: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 19 May 2026 S1

    86
    The value of ∫0π/2cos⁡3x+12cos⁡x−1dx\displaystyle\int_0^{\pi/2} \dfrac{\cos 3x + 1}{2\cos x - 1}dx is

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  2. Question 2

    Determinants and Matrices. Asked once: 13 May 2026 S2

    70
    If matrix (x1224x−332)\begin{pmatrix} x & 1 & 2 \\ 2 & 4 & x \\ -3 & 3 & 2 \end{pmatrix} is non-invertible matrix and distinct values of xx are aa and bb then 9(a2+b2)=⋯⋯⋯9(a^2 + b^2) = \cdots\cdots\cdots

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  3. Question 3

    Differential Equations. Asked once: 17 Apr 2026 S1

    75
    The tangent to the curve intersects the Y-axis at point P. A line drawn through point P is perpendicular to this tangent and passes through another point (1,0)(1, 0). The differential equation of the curve is...

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  4. Question 4

    Differentiation. Asked once: 19 May 2026 S1

    74
    If y=sin⁡−1(y⋅cos⁡2x)y = \sin^{-1}(y \cdot \cos 2x) such that dydx=2y⋅f(x)g(x)−cos⁡y\dfrac{dy}{dx} = \dfrac{2y \cdot f(x)}{g(x) - \cos y} then {f(x)}2−{g(x)}2=\{f(x)\}^2 - \{g(x)\}^2 =

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  5. Question 5

    Indefinite Integration. Asked once: 19 May 2026 S1

    80
    ∫tan⁡−1x dx=…\displaystyle\int \tan^{-1}\sqrt{x}\,dx = \ldots

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