PYQ Vault

Day 21: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. This type asked 7 times: 2 May 2023 S1, 3 May 2023 S1, 9 May 2023 S1, 13 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S2, 25 Apr 2025 S1. This one: 25 Apr 2025 S1 See all 7 of this type

    114
    ∫ex(x+5(x+6)2)dx\int e^{x}\left( \frac{x+ 5}{(x+ 6)^{2}} \right)dx is

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  2. Question 2

    Probability Distribution. Asked 6 times: 10 May 2023 S1*, 11 May 2023 S2*, 13 May 2024 S2*, 13 Apr 2026 S1*, 15 Apr 2026 S2*, 16 Apr 2026 S1 (* = numbers or wording changed that year) See all 6 times it was asked

    98
    A random variable X has the probability distribution
    X=xX = x12345678
    P(X=x)P(X = x)0.230.150.120.100.200.070.080.05
    for the events E = {X is a prime number} and F = {X ≤\le 3}, then P (E∪\cupF)=

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  3. Question 3

    Vectors. Asked 6 times: 9 May 2023 S2*, 11 May 2023 S1*, 15 May 2023 S1*, 16 May 2023 S1, 10 May 2024 S2, 11 May 2024 S1 (* = numbers or wording changed that year) See all 6 times it was asked

    148
    If a⃗\vec{a} and b⃗\vec{b} are two unit vectors such that a⃗+2b⃗\vec{a}+2\vec{b} and 5a⃗−4b⃗5\vec{a}-4\vec{b} are perpendicular to each other, then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  4. Question 4

    Determinants and Matrices. This type asked 6 times: 11 May 2023 S2, 9 May 2024 S1, 14 May 2024 S2, 17 Apr 2026 S2, 13 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 6 of this type

    67
    If A+I=(3−21−1)A + I = \begin{pmatrix} 3 & -2 \\ 1 & -1 \end{pmatrix}, then the inverse of the matrix (A−I)(A - I) is:

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  5. Question 5

    Limits. This type asked 6 times: 3 May 2023 S1, 16 May 2023 S1, 16 May 2023 S2, 19 Apr 2026 S1, 12 May 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 6 of this type

    58
    The value of lim⁡x→π4[4−(cos⁡x+sin⁡x)41−sin⁡2x]\lim_{x \to \frac{\pi}{4}}\left[\dfrac{4 - (\cos x + \sin x)^4}{1 - \sin 2x}\right] is equal to

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