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Day 481: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 17 Apr 2026 S2

    82
    If ∫ab(x2−x) dx=18, ∫abx3 dx=0\int_a^b(x^2 - x)\,dx = 18,\ \int_a^b x^3\,dx = 0, then a+ba + b is equal to

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  2. Question 2

    Determinants and Matrices. Asked once: 15 May 2023 S1

    117
    Let A and B be 3×33\times 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2−B2A2)X=O(A^{2}B^{2}-B^{2}A^{2})X = O, where X is a 3×13\times 1 column matrix and O is a 3×13\times 1 null matrix, has

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  3. Question 3

    Differentiation. Asked once: 20 Apr 2026 S1

    54
    If sec⁡−1(x2+y2x2−y2)=2a\sec^{-1}\left(\dfrac{x^2 + y^2}{x^2 - y^2}\right) = 2a such that ydydx=x⋅f(a)y\dfrac{dy}{dx} = x \cdot f(a) then the value of f(2π3)f\left(\dfrac{2\pi}{3}\right) is

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  4. Question 4

    Indefinite Integration. Asked once: 18 Apr 2026 S2

    71
    If ∫f′(x)⋅ex2 dx=(x−1)⋅ex2+k\displaystyle\int f'(x) \cdot e^{x^2}\,dx = (x - 1) \cdot e^{x^2} + k, where kk is constant of integration, then f(x)=…f(x) = \ldots

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  5. Question 5

    Limits. Asked once: 11 May 2023 S1

    108
    If f(x)={a2(x−∣x∣),x<00,x=0bx2sin⁡1x,x>0f(x) = \begin{cases} a^2(x-|x|), & x < 0 \\ 0, & x = 0 \\ bx^2\sin\frac{1}{x}, & x > 0 \end{cases} is continuous at x=0x = 0, then

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