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Day 432: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 19 May 2026 S1

    84
    The value of lim⁡n→∞(n(n+1)2n+1+n(n+2)2(2n+2)+n(n+3)3(2n+3)+⋯+12n3)\displaystyle\lim_{n \to \infty}\left(\dfrac{n}{(n + 1)\sqrt{2n + 1}} + \dfrac{n}{(n + 2)\sqrt{2(2n + 2)}} + \dfrac{n}{(n + 3)\sqrt{3(2n + 3)}} + \cdots + \dfrac{1}{2n\sqrt{3}}\right) is:

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  2. Question 2

    Determinants and Matrices. Asked once: 20 Apr 2026 S1

    66
    If A=[326112225],B=[101]A = \begin{bmatrix} 3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5 \end{bmatrix}, B = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} such that XA=BTXA = B^T and A−1Y=BA^{-1}Y = B, then XY=XY =

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  3. Question 3

    Differential Equations. Asked once: 16 Apr 2026 S2

    87
    If f(x)f(x) is a polynomial such that f(x)=[f′(x)]2f(x) = [f'(x)]^2 and f(2)=0f(2) = 0, then f(−2)=…f(-2) = \ldots

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  4. Question 4

    Differentiation. Asked once: 19 May 2026 S1

    73
    If gg is a differentiable function of xx such that g(x5)=3x7g(x^5) = 3x^7, for x≠0,x∈Rx \neq 0, x \in \mathbb{R} then g′(3125)=…g'(3125) = \ldots

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  5. Question 5

    Indefinite Integration. Asked once: 14 May 2026 S2

    81
    If ∫1+sec⁡x dx=2sin⁡−1(f(x))+c\displaystyle\int\sqrt{1 + \sec x}\,dx = 2\sin^{-1}(f(x)) + c, then

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