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Day 442: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 14 May 2026 S2

    85
    The value of the integral ∫0π/4cos⁡x1−sin⁡2x dx\displaystyle\int_0^{\pi/4}\dfrac{\cos x}{\sqrt{1 - \sin^2 x}}\,dx is

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  2. Question 2

    Determinants and Matrices. Asked once: 17 Apr 2026 S1

    65
    If the matrix A=[4132]A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix} is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?

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  3. Question 3

    Differential Equations. Asked once: 21 Apr 2025 S1

    107
    Which of the following is not a homogeneous function?

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  4. Question 4

    Differentiation. Asked once: 15 May 2026 S1

    65
    If sin⁡−1(y2)=tan⁡−1(x2)\sin^{-1}\left(\dfrac{y}{2}\right) = \tan^{-1}\left(\dfrac{x}{2}\right), ∣y∣<2|y| < 2, such that dxdy=k(4+x2)\dfrac{dx}{dy} = k(4 + x^2), then k=…k = \ldots

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  5. Question 5

    Indefinite Integration. Asked once: 13 May 2026 S2

    51
    If f(x)=1x,g(x)=3−2x−x2f(x) = \dfrac{1}{\sqrt{x}}, g(x) = 3 - 2x - x^2 then ∫[(f∘g)(ex)]⋅ex dx=⋯⋯⋯\displaystyle\int[(f \circ g)(e^x)] \cdot e^x\,dx = \cdots\cdots\cdots

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