PYQ Vault

Day 259: CBSE Class 12 Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1

    Integrals. Asked once: 2024 (same type asked 5 times)

    23 (a)
    Evaluate : ∫0π/2sin⁡2xcos⁡3x dx\int\limits_{0}^{\pi/2} \sin 2x \cos 3x\, dx

  2. Question 2 (case study, 4 parts)

    Probability. Asked once: 2024 (same type asked 5 times)

    Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals. Previous records state that the probability of an airplane crash is 0⋅00001%0{\cdot}00001\%. Further, there are 95% chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive. Let E1E_1 be the event that there is a plane crash and E2E_2 be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions :
    38 (i)
    Find the probability that the airplane will not crash.
    38 (ii)
    Find P(A ∣ E1)+P(A ∣ E2)P(A \,|\, E_1) + P(A \,|\, E_2).
    38 (iii) (a)
    Find P(A).
    38 (iii) (b)
    Find P(E2 ∣ A)P(E_2 \,|\, A).

  3. Question 3

    Probability. Asked once: 2023 (same type asked 5 times)

    3
    If for two events A and B, P(A−B)=15P(A - B) = \frac{1}{5} and P(A)=35P(A) = \frac{3}{5}, then P(BA)P\left(\frac{B}{A}\right) is equal to

    Tap an option to check your answer.

  4. Question 4 (case study, 2 parts)

    Probability. Asked once: 2022 (same type asked 5 times)

    In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9 to 1 in sequential order moving outwards. Archer A is likely to earn 10 points with a probability of 0⋅80{\cdot}8 and Archer B is likely the earn 10 points with a probability of 0⋅90{\cdot}9. Based on the above information, answer the following questions : If both of them hit the Archery target, then find the probability that
    14 (a)
    exactly one of them earns 10 points.
    14 (b)
    both of them earn 10 points.

  5. Question 5

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

    22 (a)
    If f(x)={x2,if x≥1x,if x<1f(x) = \begin{cases} x^2, & \text{if } x \ge 1 \\ x, & \text{if } x < 1 \end{cases}, then show that f is not differentiable at x=1x = 1.