PYQ Vault

Day 101: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Integrals. Asked once: 2026 (same type asked 5 times)

    12
    ∫dxsec⁡x+tan⁡x\displaystyle\int \dfrac{dx}{\sec x + \tan x} is equal to

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  2. Question 2 (case study, 4 parts)

    Probability. Asked once: 2026 (same type asked 5 times)

    A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII. As per the data collected, 40% students appearing in the examination were dropouts and the remaining students were regular students of class XII. Of the dropouts, 5% qualify the examination while 10% of the regular students qualify the examination. Based on the above information, answer the following questions.
    37 (i)
    Find the probability that a student selected at random is a regular student.
    37 (ii)
    A student is selected at random from a group of dropout students. What is the probability that the student will not qualify the examination ?
    37 (iii) (a)
    A student selected at random qualified the examination. Find the probability that student is not a dropout.
    37 (iii) (b)
    A student selected at random did not qualify the examination. Find the probability that the student was a regular student.

  3. Question 3

    Probability. Asked once: 2025 (same type asked 5 times)

    17
    If A and B are two events such that P(B)=15P(B) = \dfrac{1}{5}, P(A ∣ B)=23P(A\ |\ B) = \dfrac{2}{3} and P(A∪B)=35P(A \cup B) = \dfrac{3}{5}, then P(A)P(A) is :

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  4. Question 4

    Probability. Asked once: 2026 (same type asked 5 times)

    18
    The probability that it will rain tomorrow in cities A, B and C is 60%, 70% and 80% respectively. The probability that it will rain tomorrow in at least one of the cities is :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2024 (same type asked 5 times)

    35 (b)
    Two vertices of the parallelogram ABCD are given as A(−1,2,1)A(-1, 2, 1) and B(1,−2,5)B(1, -2, 5). If the equation of the line passing through C and D is x−41=y+7−2=z−82\dfrac{x - 4}{1} = \dfrac{y + 7}{-2} = \dfrac{z - 8}{2}, then find the distance between sides AB and CD. Hence, find the area of parallelogram ABCD.