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Day 467: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: 20 Apr 2026 S1

    82
    If ∫01dxx+1−x=2k\int_0^1\dfrac{dx}{\sqrt{x + 1} - \sqrt{x}} = \sqrt{2}k, then the value of kk is...

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  2. Question 2

    Determinants and Matrices. Asked once: 14 May 2024 S1

    129
    Let A=(2−102)A=\begin{pmatrix}2&-1\\0&2\end{pmatrix}. If B=I−3C1(adj A)+3C2(adj A)2−3C3(adj A)3B=I-{}^3C_1(\text{adj}\,A)+{}^3C_2(\text{adj}\,A)^2-{}^3C_3(\text{adj}\,A)^3, then the sum of all elements of the matrix BB is

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  3. Question 3

    Differentiation. Asked once: 12 May 2026 S2

    69
    If f(x)=∣x2sin⁡xex21−1pp21∣f(x) = \begin{vmatrix} x^2 & \sin x & e^x \\ 2 & 1 & -1 \\ p & p^2 & 1 \end{vmatrix} then f′′(0)=f''(0) =

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  4. Question 4

    Indefinite Integration. Asked once: 20 Apr 2026 S2

    81
    ∫(x21+x6+x3)(2x18+7x3+14)13 dx=\displaystyle\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\,dx =

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  5. Question 5

    Limits. Asked once: 14 May 2024 S2

    122
    Let f(x)=5−∣x−2∣f(x) = 5 - |x-2| and g(x)=∣x+1∣g(x) = |x+1|, x∈Rx\in\mathbb{R}. If f(x)f(x) attains maximum at α\alpha and g(x)g(x) attains minimum at β\beta, then lim⁡x→−αβ(x−1)(x2−5x+6)x2−6x+8\lim_{x\to -\alpha\beta}\frac{(x-1)(x^2-5x+6)}{x^2-6x+8} is equal to

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