PYQ Vault

Day 243: CBSE Class 12 Maths

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

  1. Question 1

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

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : ∫2810−xx+10−x dx=3\displaystyle\int_{2}^{8} \dfrac{\sqrt{10 - x}}{\sqrt{x} + \sqrt{10 - x}}\,dx = 3 Reason (R) : ∫abf(x) dx=∫abf(a+b−x) dx\displaystyle\int_{a}^{b} f(x)\,dx = \int_{a}^{b} f(a + b - x)\,dx

    Tap an option to check your answer.

  2. Question 2

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

    28
    Find : ∫sec⁡3θ dθ\displaystyle\int \sec^{3}\theta\,d\theta

  3. Question 3

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

    11
    ∫cos⁡2x−cos⁡2θcos⁡x−cos⁡θ dx\displaystyle\int \dfrac{\cos 2x - \cos 2\theta}{\cos x - \cos \theta}\ dx is equal to :

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  4. Question 4 (case study, 2 parts)

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

    A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant and 8 seeds of radish plant. The shopkeeper assured him of germination probabilities of brinjal, cabbage and radish to be 25%, 35% and 40% respectively. But before he could plant the seeds, they got mixed up in the bag and he had to sow them randomly. Based upon the above information, answer the following questions :
    38 (i)
    Calculate the probability of a randomly chosen seed to germinate.
    38 (ii)
    What is the probability that it is a cabbage seed, given that the chosen seed germinates ?

  5. Question 5

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

    11
    Let E and F be two events such that P(E)=0⋅1P(E) = 0{\cdot}1, P(F)=0⋅3P(F) = 0{\cdot}3, P(E∪F)=0⋅4P(E \cup F) = 0{\cdot}4, then P(F ∣ E)P(F\,|\,E) is :

    Tap an option to check your answer.