PYQ Vault

Day 70: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. Asked once: 2026 (same type asked 4 times)

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

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  2. Question 2

    Probability. Asked once: 2026 (same type asked 4 times)

    31
    In a school, the probability of holding a debate competition is 13\dfrac{1}{3} and that of a quiz competition is 23\dfrac{2}{3}. In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.

  3. Question 3

    Probability. Asked once: 2026 (same type asked 4 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is 23\frac{2}{3}. Reason (R) : For any two events A and B, P(A∣B)=P(A∪B)P(B)P(A|B) = \frac{P(A \cup B)}{P(B)}

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  4. Question 4

    Probability. Asked once: 2025 (same type asked 4 times)

    30 (b)
    Two dice are thrown. Defined are the following two events A and B : A={(x,y):x+y=9}A = \{(x, y) : x + y = 9\}, B={(x,y):x≠3}B = \{(x, y) : x \ne 3\}, where (x,y)(x, y) denote a point in the sample space. Check if events A and B are independent or mutually exclusive.

  5. Question 5

    Three Dimensional Geometry. Asked once: 2026 (same type asked 4 times)

    23
    Find the co-ordinates of foot of perpendicular drawn from (0, 0, 0) to line x1=y+1−1=z−3−2\dfrac{x}{1} = \dfrac{y + 1}{-1} = \dfrac{z - 3}{-2}.