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Day 63: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. This type asked 4 times: 10 May 2024 S1, 13 May 2024 S2, 19 Apr 2025 S1, 26 Apr 2025 S1. This one: 26 Apr 2025 S1 See all 4 of this type

    134
    The following is p.d.f. of continuous random variable X f(x)={x8, if 0<x<40, otherwise f(x) =\left\{ \begin{matrix} \frac{x}{8} & ,\text{~if~}0 <x< 4 \\ 0 & ,\text{~otherwise~} \end{matrix} \right..Then F(0.5),F(1.7)F(0.5),F(1.7) and F(5)F(5) is respectively

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  2. Question 2

    Applications of Derivative. This type asked 4 times: 16 May 2023 S1, 12 May 2024 S1, 19 Apr 2025 S1, 25 Apr 2025 S2. This one: 25 Apr 2025 S2 See all 4 of this type

    141
    The angle θ\theta, at which the curves y=3xy=3^{x} and y=7xy=7^{x} intersect, is given by

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  3. Question 3

    Vectors. This type asked 4 times: 3 May 2023 S1, 15 May 2023 S2, 22 Apr 2025 S2, 25 Apr 2025 S1. This one: 25 Apr 2025 S1 See all 4 of this type

    137
    If the area of a parallelogram whose diagonals are represented by vectors 3i^+λj^+2k^3\widehat{i}+\lambda\widehat{j}+ 2\widehat{k} and i^−2j^+3k^\widehat{i}- 2\widehat{j}+ 3\widehat{k} is 1172\frac{\sqrt{117}}{2} sq. units, then λ=\lambda=

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  4. Question 4

    Vectors. This type asked 4 times: May 2021 S1, 10 May 2023 S2, 10 May 2024 S1, 22 Apr 2025 S2. This one: 22 Apr 2025 S2 See all 4 of this type

    150
    The projection of the line segment joining P(2,−1,0)P(2, - 1,0) and Q(3,2,−1)Q(3,2, - 1) on the line whose direction ratios are 1,2,21,2,2 is

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  5. Question 5

    Applications of Derivative. This type asked 4 times: 16 May 2023 S1, 11 May 2024 S1, 21 Apr 2025 S1, 22 Apr 2025 S1. This one: 22 Apr 2025 S1 See all 4 of this type

    140
    If f(x)=x⋅ex(1−x)f(x) =x\cdot e^{x(1 -x)}, then f(x)f(x) is

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