PYQ Vault

Day 32: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    3
    If A and B are skew-symmetric matrices of same order, then AB′+BA′AB' + BA' is a/an :

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  2. Question 2

    Matrices. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    27
    If A=[2012131−10]A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix}, then compute A2−5A+4 IA^2 - 5A + 4\,I.
  3. Question 3

    Matrices. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    2
    Let A=[aij]A = [a_{ij}] be a 2×22 \times 2 matrix whose elements are given by aij=(i+2j)23a_{ij} = \dfrac{(i + 2j)^2}{3}. Then A′A' is given by :

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  4. Question 4

    Probability. This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026

    31 (a)
    Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the probability that the ball drawn from one of the bags is a red ball.
  5. Question 5

    Probability. This type asked 4 times: 2022, 2023, 2025, 2026. This one: 2026

    31 (a)
    A die is rolled. Consider events : A={1, 2, 5}A = \{1,\ 2,\ 5\}, B={3, 5}B = \{3,\ 5\}, C={2, 3, 4, 5}C = \{2,\ 3,\ 4,\ 5\} and hence find : (i) P(A ∣ C)P(A\,|\,C) and P(C ∣ A)P(C\,|\,A) (ii) P(A∩B ∣ C)P(A \cap B\,|\,C) and P(A∪B ∣ C)P(A \cup B\,|\,C)