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Day 465: MHT-CET Maths

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

  1. Question 1

    Sets, Relations and Functions. Asked once: 25 Apr 2025 S2

    136
    Let f:R−{2}→R−{1}f:\mathbb{R}\mathbf{- \{ 2\} \rightarrow}\mathbb{R}\mathbf{- \{ 1\}} defined by f(x)=x−3x−2f(x) =\frac{x- 3}{x- 2} and g:R→Rg:\mathbb{R}\rightarrow\mathbb{R} defined by g(x)=3x−2g(x) = 3x- 2, then sum of all values of xx for which f−1(x)+g−1(x)=196f^{- 1}(x) +g^{- 1}(x) =\frac{19}{6} is

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  2. Question 2

    Straight Line. Asked once: 22 Apr 2025 S1

    105
    From the following options, the nearest line to the origin is ....

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  3. Question 3

    Trigonometric Functions. Asked once: 13 May 2026 S1

    53
    In △ABC\triangle ABC with usual notations, if a,c,ba, c, b are in Arithmetic Progression (A.P.), then the value of acos⁡B−bcos⁡Aa−b\dfrac{a\cos B - b\cos A}{a - b} is:

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  4. Question 4

    Trigonometry - II. Asked once: 13 Apr 2026 S2

    54
    If cos⁡(θ−α)=a\cos(\theta - \alpha) = a and sin⁡(θ−β)=b\sin(\theta - \beta) = b, then the value of cos⁡2(α−β)+2absin⁡(α−β)+cos⁡2(θ−α)\cos^2(\alpha - \beta) + 2ab\sin(\alpha - \beta) + \cos^2(\theta - \alpha) is...

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  5. Question 5

    Vectors. Asked once: 13 May 2026 S1

    95
    The sum of the lengths of the projections of 2i^+3j^+4k^2\hat{i} + 3\hat{j} + 4\hat{k} on the coordinate axes is

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