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Day 91: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. This type asked 3 times: 13 Apr 2026 S2, 15 Apr 2026 S2, 16 Apr 2026 S2. This one: 16 Apr 2026 S2 See all 3 of this type

    64
    If A=[aij]3×3A = [a_{ij}]_{3 \times 3} is a matrix such that aij=∣2i−5j∣a_{ij} = |2i - 5j|, where ∣⋅∣|\cdot| denotes the modulus function, then the element in the 2nd2^{nd} row and 3rd3^{rd} column of A−1A^{-1} is ...

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  2. Question 2

    Trigonometric Functions. This type asked 3 times: 11 May 2023 S1, 9 May 2024 S2, 16 Apr 2026 S2. This one: 16 Apr 2026 S2 See all 3 of this type

    66
    The value of cot⁡−1[1−sin⁡x+1+sin⁡x1−sin⁡x−1+sin⁡x]\cot^{-1}\left[\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}\right], where x∈(0,π2)x \in \left(0, \dfrac{\pi}{2}\right) is...

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  3. Question 3

    Applications of Derivative. This type asked 3 times: 9 May 2023 S1, 15 Apr 2026 S2, 16 Apr 2026 S1. This one: 16 Apr 2026 S1 See all 3 of this type

    75
    The minimum value of log⁡xx\dfrac{\log x}{x} in the interval (2,∞)(2, \infty) is

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  4. Question 4

    Line and Plane. This type asked 3 times: 25 Apr 2025 S2, 26 Apr 2025 S2, 16 Apr 2026 S1. This one: 16 Apr 2026 S1 See all 3 of this type

    92
    The lines x−1−1=y+21=z−3−2\dfrac{x - 1}{-1} = \dfrac{y + 2}{1} = \dfrac{z - 3}{-2} and x−11=y+21=z+1−2\dfrac{x - 1}{1} = \dfrac{y + 2}{1} = \dfrac{z + 1}{-2} are

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  5. Question 5

    Sets, Relations and Functions. This type asked 3 times: 2 May 2023 S1, 10 May 2023 S2, 16 Apr 2026 S1. This one: 16 Apr 2026 S1 See all 3 of this type

    69
    If f(x)=4x+36x−4,x≠23f(x) = \dfrac{4x + 3}{6x - 4}, x \neq \dfrac{2}{3} and (fof)(x)=g(x)(x) = g(x) where g:R−{23}→R−{23}g : \mathbb{R} - \left\{\dfrac{2}{3}\right\} \to \mathbb{R} - \left\{\dfrac{2}{3}\right\}, then (g∘g∘g∘g∘g)(3)=(g \circ g \circ g \circ g \circ g)(3) =

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