PYQ Vault

Day 49: CBSE Class 12 Maths

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

  1. Question 1

    Relations and Functions. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    27
    Let R be a relation defined over N, where N is set of natural numbers, defined as “mRn if and only if m is a multiple of n, m, n ∈\in N.” Find whether R is reflexive, symmetric and transitive or not.

  2. Question 2

    Vector Algebra. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    25 (a)
    Two friends while flying kites from different locations, find the strings of their kites crossing each other. The strings can be represented by vectors a⃗=3i^+j^+2k^\vec{a} = 3\hat{i} + \hat{j} + 2\hat{k} and b⃗=2i^−2j^+4k^\vec{b} = 2\hat{i} - 2\hat{j} + 4\hat{k}. Determine the angle formed between the kite strings. Assume there is no slack in the strings.

  3. Question 3

    Vector Algebra. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    24 (a)
    If a⃗\vec{a} and b⃗\vec{b} are position vectors of point A and point B respectively, find the position vector of point C on BA produced such that BC=3BABC = 3BA.

  4. Question 4

    Probability. This type asked 3 times: 2022, 2023, 2024. This one: 2023

    31 (b)
    There are two coins. One of them is a biased coin such that P (head) : P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.

  5. Question 5 (case study, 4 parts)

    Application of Derivatives. This type asked 2 times: 2024, 2026. This one: 2026

    An online delivery company in a city has 5000 subscribers and collects annual subscription fees of ₹ 300 per subscriber for unlimited free deliveries. The company wishes to increase the annual subscription fee. It is predicted that, for every increase of ₹ 1, ten subscribers will discontinue. Assume that the company increased the annual fee by ₹ xx. Based on the given information, answer the following questions :
    36 (i)
    How many subscribers will discontinue after an increase of ₹ xx in annual fee ?
    36 (ii)
    If R(x)R(x) denotes the total revenue collected after the increase of ₹ xx in subscription fee, express R(x)R(x) as a function of xx.
    36 (iii) (a)
    Find the value of xx for which R(x)R(x) is maximum.
    36 (iii) (b)
    Find the sub-intervals of (0, 5000) in which R(x)R(x) is increasing and decreasing.