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Day 452: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 26 Apr 2025 S1

    116
    If the function f(x)={cos⁡ax−cos⁡bxcos⁡cx−cos⁡bx, if x≠0 −1, if x=0f(x) =\left\{ \begin{matrix} \dfrac{\cos ax- \cos bx}{\cos cx- \cos bx} & ,\ \text{if } x\neq 0 \ -1 & ,\ \text{if } x = 0 \end{matrix} \right. is continuous at x=0x = 0, then a2,b2,c2a^{2}, b^{2}, c^{2} are in

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  2. Question 2

    Line and Plane. Asked once: 12 May 2026 S1

    94
    A line passing through A(1,3,2)A(1, 3, 2) and parallel to the line x−21=y−42=z−61\dfrac{x - 2}{1} = \dfrac{y - 4}{2} = \dfrac{z - 6}{1} intersects the plane x−y+3z−6=0x - y + 3z - 6 = 0 at point B. Another line through B and perpendicular to the plane x−y+3z−6=0x - y + 3z - 6 = 0 intersects the plane 2x−y+z+4=02x - y + z + 4 = 0 at the point C. Then the equation of median of ΔABC\Delta ABC through the vertex A is ...

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  3. Question 3

    Measures of Dispersion. Asked once: 3 May 2023 S1

    125
    The mean of nn observations is xˉ\bar{x}. If three observations n+1,n−1,2n−1n+1, n-1, 2n-1 are added such that mean remains same, then value of nn is

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  4. Question 4

    Pair of Straight Lines. Asked once: 12 May 2024 S2

    117
    If the pair of lines given by (xcos⁡α+ysin⁡α)2=(x2+y2)sin⁡2α(x\cos\alpha + y\sin\alpha)^2 = (x^2+y^2)\sin^2\alpha are perpendicular to each other, then α\alpha is

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  5. Question 5

    Permutations and Combinations. Asked once: 26 Apr 2025 S1

    139
    The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is

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