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Day 35: MHT-CET Maths

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

  1. Question 1

    Differentiation. This type asked 5 times: 9 May 2023 S2, 11 May 2023 S1, 9 May 2024 S1, 20 Apr 2026 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 5 of this type

    75
    If 3x2+4xy+5y2=03x^2 + 4xy + 5y^2 = 0, then dydx=…\dfrac{dy}{dx} = \ldots

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  2. Question 2

    Applications of Definite Integral. This type asked 5 times: May 2021 S1, 4 May 2023 S1, 16 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    84
    The area of the region bounded by the curves y2=9xy^2 = 9x and x2=9yx^2 = 9y

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  3. Question 3

    Determinants and Matrices. This type asked 5 times: May 2022 S1, 23 Apr 2025 S1, 15 Apr 2026 S2, 16 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    69
    If A−1=[3−11−156−55−22]A^{-1} = \begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix} and B=[12−2−1300−21]B = \begin{bmatrix} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{bmatrix}, then (AB)−1=(AB)^{-1} =

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  4. Question 4

    Probability Distribution. This type asked 5 times: 14 May 2024 S1, 22 Apr 2025 S1, 20 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    99
    Let X be a random variable with the probability density function defined by f(x)=1x2,1<x<∞f(x) = \dfrac{1}{x^2}, 1 < x < \infty =0= 0 otherwise. If C1={x:1<x<2}C_1 = \{x : 1 < x < 2\} and C2={x:4<x<5}C_2 = \{x : 4 < x < 5\} then P(C1∪C2)=P(C_1 \cup C_2) =

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  5. Question 5

    Sets, Relations and Functions. This type asked 5 times: May 2022 S1, 11 May 2023 S1, 15 May 2023 S2, 26 Apr 2025 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    51
    If [⋅][\cdot] represents the greatest integer function of less than or equal to type then the solution set of the equation [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0 is

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