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Day 513: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 22 Apr 2025 S2

    103
    The distance of the plane r‾=(i^−j^)+λ(i^+j^+k^)+μ(i^−2j^+3k^)\overline{r}= (\widehat{i}-\widehat{j}) + \lambda(\widehat{i}+\widehat{j}+\widehat{k}) + \mu(\widehat{i}- 2\widehat{j}+ 3\widehat{k}) from the origin is

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  2. Question 2

    Probability Distribution. Asked once: May 2021 S1

    129
    If f(x)=k⋅2xf(x) = k\cdot 2^x is a probability distribution of a random variable XX that can take on the values x=0,1,2,3,4x = 0, 1, 2, 3, 4, then kk is equal to

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  3. Question 3

    Trigonometric Functions. Asked once: 25 Apr 2025 S1

    150
    If in triangle ABC , with usual notations sin⁡A2⋅sin⁡C2=sin⁡B2\sin\frac{A}{2}\cdot \sin\frac{C}{2}= \sin\frac{B}{2} and 2 s is the perimeter of the triangle, then the value of ss is

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  4. Question 4

    Trigonometry - II. Asked once: 2 May 2023 S2

    107
    If α+β+γ=π\alpha+\beta+\gamma = \pi, then the expression sin⁡2α+sin⁡2β−sin⁡2γ\sin^2\alpha + \sin^2\beta - \sin^2\gamma has the value

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  5. Question 5

    Vectors. Asked once: 15 Apr 2026 S1

    89
    If ABCDEF is a regular hexagon and AB‾+AC‾+AD‾+AE‾+AF‾=pAD‾=qAO‾\overline{AB} + \overline{AC} + \overline{AD} + \overline{AE} + \overline{AF} = p\overline{AD} = q\overline{AO}, where O is the center of the hexagon, then the values of pp and qq respectively are

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