PYQ Vault

Day 253: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Integrals. Asked once: 2023 (same type asked 4 times)

    28 (b)
    Evaluate : ∫0π/2sin⁡x cos⁡5x dx\displaystyle\int_0^{\pi/2} \sqrt{\sin x}\, \cos^5 x\, dx

  2. Question 2

    Integrals. Asked once: 2024 (same type asked 4 times)

    28 (b)
    Find : ∫2x+1(x+1)2 (x−1) dx\displaystyle\int \dfrac{2x + 1}{(x + 1)^2\,(x - 1)}\, \mathrm{d}x

  3. Question 3

    Probability. Asked once: 2022 (same type asked 4 times)

    2
    A coin is tossed twice. The following table shows the probability distribution of number of tails :
    X012
    P(X)K6K9K
    (a) Find the value of K. (b) Is the coin tossed biased or unbiased ? Justify your answer.

  4. Question 4

    Probability. Asked once: 2022 (same type asked 4 times)

    5
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spade cards.

  5. Question 5

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

    8 (b)
    Find the general solution of the differential equation xdydx=y(log⁡y−log⁡x+1)x \dfrac{dy}{dx} = y(\log y - \log x + 1).