PYQ Vault

Day 36: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    32 (a)
    Find : ∫x2+1(x−1)2(x+3) dx\displaystyle\int \dfrac{x^2 + 1}{(x - 1)^2 (x + 3)}\, dx

  2. Question 2

    Integrals. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    26
    Find : ∫x1+x3/2 dx\int \frac{\sqrt{x}}{1 + \sqrt{x^{3/2}}}\, dx

  3. Question 3

    Probability. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    30 (a)
    The probability distribution for the number of students being absent in a class on a Saturday is as follows :
    X0245
    P(X)p2p3pp
    Where X is the number of students absent. (i) Calculate p. (ii) Calculate the mean of the number of absent students on Saturday.

  4. Question 4

    Probability. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    29 (b)
    A coin is tossed twice. Let X be a random variable defined as number of heads minus number of tails. Obtain the probability distribution of X and also find its mean.

  5. Question 5

    Three Dimensional Geometry. This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025

    9
    The equation of a line parallel to the vector 3i^+j^+2k^3\hat{i} + \hat{j} + 2\hat{k} and passing through the point (4,−3,7)(4, -3, 7) is :

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