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Day 471: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 11 May 2024 S1

    136
    Let ω≠1\omega \neq 1 be a cube root of unity and S be the set of all non-singular matrices of the form (1abω1cω2ω1)\begin{pmatrix}1&a&b\\\omega&1&c\\\omega^2&\omega&1\end{pmatrix} where each of a, b and c is either ω\omega or ω2\omega^2, then the number of distinct matrices in the set S is

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  2. Question 2

    Differentiation. Asked once: 12 May 2026 S2

    73
    If y=(x+1x)2y = \left(\sqrt{x} + \dfrac{1}{\sqrt{x}}\right)^2 and dydx=34\dfrac{dy}{dx} = \dfrac{3}{4}, then the value of xx is...

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  3. Question 3

    Indefinite Integration. Asked once: 20 Apr 2026 S1

    80
    The value of ∫sin⁡4xcos⁡3x dx\displaystyle\int\sin 4x\cos 3x\,dx is

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  4. Question 4

    Limits. Asked once: 12 May 2024 S2

    127
    lim⁡x→0xcot⁡4xsin⁡2x⋅cot⁡2(2x)\lim_{x \to 0} \frac{x\cot 4x}{\sin^2 x \cdot \cot^2(2x)} is equal to

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  5. Question 5

    Line and Plane. Asked once: 18 Apr 2026 S1

    92
    The line ℓ\ell passes through the point (2,1,1)(2, 1, 1) and is parallel to the plane x+y+2z=18x + y + 2z = 18. If line ℓ\ell intersects the line x+23=y+1−1=z−21\dfrac{x + 2}{3} = \dfrac{y + 1}{-1} = \dfrac{z - 2}{1}, then equation of the line ℓ\ell is...

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