PYQ Vault

Day 234: CBSE Class 12 Maths

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

  1. Question 1

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

    12
    The value of ∫−11x ∣x∣ dx\displaystyle\int_{-1}^{1} x\,|x|\, dx is :

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  2. Question 2

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

    6
    ∫0π/2sin⁡x−cos⁡x1+sin⁡xcos⁡x dx\displaystyle\int_0^{\pi/2} \dfrac{\sin x - \cos x}{1 + \sin x \cos x}\, dx is equal to :

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  3. Question 3

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

    12
    The value of ∫1elog⁡x dx\displaystyle\int_{1}^{e} \log x\, \mathrm{d}x is :

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  4. Question 4

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

    3
    ∫dxsin⁡2xcos⁡2x\displaystyle\int \dfrac{dx}{\sin^2 x \cos^2 x} is equal to

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  5. Question 5 (case study, 2 parts)

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

    A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities 10%, 20% and 70% respectively. A customer after availing loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate and variable rate is 5%, 3% and 1% respectively. Based on the above information, answer the following :
    38 (i)
    What is the probability that a customer after availing the loan will default on the loan repayment ?
    38 (ii)
    A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest ?