PYQ Vault

Day 26: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    10
    ∫11+cos⁡2x dx\displaystyle\int \dfrac{1}{\sqrt{1 + \cos 2x}}\,dx is equal to :

    Tap an option to check your answer.

  2. Question 2 (case study, 4 parts)

    Probability. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information, answer the following questions :
    36 (i)
    What is the probability that selected person is a female ?
    36 (ii)
    If a male person is selected, what is the probability that he will not be suffering from lung problems ?
    36 (iii) (a)
    A person selected at random is detected with lung complications. Find the probability that selected person is a female.
    36 (iii) (b)
    A person selected at random is not having lung problems, find the probability that the person is a male.

  3. Question 3

    Probability. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    18
    If 3P(A)=P(B)=353P(A) = P(B) = \dfrac{3}{5} and P(A ∣ B)=23P(A\,|\,B) = \dfrac{2}{3}, then P(A∪B)P(A \cup B) is :

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  4. Question 4

    Probability. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    18
    The probability that a particular item is available in three shops A, B and C is 45\dfrac{4}{5}, 34\dfrac{3}{4} and 23\dfrac{2}{3} respectively. If a person visits all the three shops to buy the item, then what is the probability that it will be available in at least one of the shops ?

    Tap an option to check your answer.

  5. Question 5

    Three Dimensional Geometry. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    32
    Show that line AB passing through points A(0, 4, 1), B(2, 3, -1) and the line CD passing through points C(4, 5, 0), D(2, 6, 2) are parallel. Also, find distance between them.