PYQ Vault

Day 207: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

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

    Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record. Let A1A_1 : People with good health, A2A_2 : People with average health, and A3A_3 : People with poor health. During a pandemic, the data expressed that the chances of people contracting the disease from category A1A_1, A2A_2 and A3A_3 are 25%, 35% and 50%, respectively. Based upon the above information, answer the following questions :
    38 (i)
    A person was tested randomly. What is the probability that he/she has contracted the disease ?
    38 (ii)
    Given that the person has not contracted the disease, what is the probability that the person is from category A2A_2 ?

  2. Question 2

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

    2
    If P(A∪B)=0⋅9P(A \cup B) = 0{\cdot}9 and P(A∩B)=0⋅4P(A \cap B) = 0{\cdot}4, then P(A‾)+P(B‾)P(\overline{A}) + P(\overline{B}) is :

    Tap an option to check your answer.

  3. Question 3

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

    18
    A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0⋅100{\cdot}10, member B does not turn up is 0⋅200{\cdot}20 and member C does not turn up is 0⋅050{\cdot}05. The probability of the meeting being cancelled is :

    Tap an option to check your answer.

  4. Question 4

    Continuity and Differentiability. Asked once: 2023 (same type asked 4 times)

    21 (a)
    Find the value of k for which the function f given as f(x)={1−cos⁡x2x2,if x≠0k,if x=0f(x) = \begin{cases} \dfrac{1 - \cos x}{2x^2}, & \text{if } x \ne 0 \\ k, & \text{if } x = 0 \end{cases} is continuous at x=0x = 0.

  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)

    26 (b)
    Find the value of a and b so that function f defined as : f(x)={x−2∣x−2∣+a,if x<2a+b,if x=2x−2∣x−2∣+b,if x>2f(x) = \begin{cases} \dfrac{x - 2}{|x - 2|} + a, & \text{if } x < 2 \\ a + b, & \text{if } x = 2 \\ \dfrac{x - 2}{|x - 2|} + b, & \text{if } x > 2 \end{cases} is a continuous function.