PYQ Vault

Day 163: CBSE Class 12 Maths

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

  1. Question 1

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

    32 (b)
    Evaluate : ∫0πxtan⁡xsec⁡x+tan⁡x dx\displaystyle\int_{0}^{\pi} \dfrac{x \tan x}{\sec x + \tan x}\, dx

  2. Question 2

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

    26
    Evaluate : ∫01log⁡(1+x2) dx\int_{0}^{1} \log(1 + x^2)\,dx

  3. Question 3

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

    10
    ∫1+cos⁡x1−cos⁡x dx\displaystyle\int \sqrt{\dfrac{1 + \cos x}{1 - \cos x}}\,dx is equal to :

    Tap an option to check your answer.

  4. Question 4 (case study, 4 parts)

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

    Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production share in the market is 60%, 30% and 10% respectively. Of their respective production capacities, 20%, 10% and 5% cars respectively are electric (or battery operated). Based on the above, answer the following :
    37 (i) (a)
    What is the probability that a randomly selected car is an electric car ?
    37 (i) (b)
    What is the probability that a randomly selected car is a petrol car ?
    37 (ii)
    A car is selected at random and is found to be electric. What is the probability that it was manufactured by Comet ?
    37 (iii)
    A car is selected at random and is found to be electric. What is the probability that it was manufactured by Amber or Bonzi ?

  5. Question 5

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

    7
    Let M and N be two events such that P(M) = 0.6, P(N) = 0.2 and P(M∩N)=0.5P(M \cap N) = 0.5, then P(M′/N′)P(M'/N') is

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