PYQ Vault

Day 80: CBSE Class 12 Maths

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

  1. Question 1

    Probability. Asked once: 2025 (same type asked 3 times)

    29 (b)
    In a city, a survey was conducted among residents about their preferred mode of commuting. It was found that 50% people preferred using public transport, 35% preferred using a bicycle and 20% use both public transport and a bicycle. If a person is selected at random, find the probability that : (i) The person uses only public transport. (ii) The person uses a bicycle, given that they also use the public transport. (iii) The person uses neither public transport nor a bicycle.

  2. Question 2

    Relations and Functions. Asked once: 2026 (same type asked 3 times)

    33
    Show that a function f:R+→A⊂Nf : R_+ \to A \subset N, defined as f(x)=4x2+12x+15f(x) = 4x^2 + 12x + 15 is one-one. Find set A so that f is onto where R+=[0,∞)R_+ = [0, \infty). Also, find if there exists a∈R+a \in R_+ such that f(a)=7f(a) = 7. Justify.

  3. Question 3

    Relations and Functions. Asked once: 2026 (same type asked 3 times)

    5
    A relation R on set A = {1,2,3}\{1, 2, 3\} is defined as R = {(1,3),(3,3),(1,1),(2,2),(3,1)}\{(1, 3), (3, 3), (1, 1), (2, 2), (3, 1)\} is

    Tap an option to check your answer.

  4. Question 4 (case study, 4 parts)

    Relations and Functions. Asked once: 2025 (same type asked 3 times)

    A school is organizing a debate competition with participants as speakers S={S1,S2,S3,S4}S = \{S_1, S_2, S_3, S_4\} and these are judged by judges J={J1,J2,J3}J = \{J_1, J_2, J_3\}. Each speaker can be assigned one judge. Let R be a relation from set S to J defined as R={(x,y):speaker x is judged by judge y, x∈S, y∈J}R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y,\ x \in S,\ y \in J\}. Based on the above, answer the following :
    36 (i)
    How many relations can be there from S to J ?
    36 (ii)
    A student identifies a function from S to J as f={(S1,J1),(S2,J2),(S3,J2),(S4,J3)}f = \{(S_1, J_1), (S_2, J_2), (S_3, J_2), (S_4, J_3)\} Check if it is bijective.
    36 (iii) (a)
    How many one-one functions can be there from set S to set J ?
    36 (iii) (b)
    Another student considers a relation R1={(S1,S2),{S2,S4)}R_1 = \{(S_1, S_2), \{S_2, S_4)\} in set S. Write minimum ordered pairs to be included in R1R_1 so that R1R_1 is reflexive but not symmetric.

  5. Question 5

    Relations and Functions. Asked once: 2025 (same type asked 3 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : Let Z be the set of integers. A function f:Z→Zf : Z \to Z defined as f(x)=3x−5f(x) = 3x - 5, ∀x∈Z\forall x \in Z is a bijective. Reason (R) : A function is a bijective if it is both surjective and injective.

    Tap an option to check your answer.