PYQ Vault

Day 43: 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: 2024, 2025, 2026. This one: 2026

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

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  2. Question 2 (case study, 4 parts)

    Relations and Functions. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set A={G1, G2, G3, G4}A = \{G_1,\ G_2,\ G_3,\ G_4\}, Boy students belong to Set B={B1, B2, B3}B = \{B_1,\ B_2,\ B_3\}. Based on the above information, answer the following questions :
    36 (i)
    How many relations are possible from Set A →\to Set B ?
    36 (ii)
    Let R be a relation from A →\to B such that R={(G1, B1), (G2, B2), (G3, B2), (G4, B3), (G1, B2)}R = \{(G_1,\ B_1),\ (G_2,\ B_2),\ (G_3,\ B_2),\ (G_4,\ B_3),\ (G_1,\ B_2)\}. Is R an injective function ? Justify your answer.
    36 (iii) (a)
    Let the relation R from A →\to A be such that R={(x, y), x, y∈AR = \{(x,\ y),\ x,\ y \in A, x and y are students from the same colony in the city}\} Verify if R is an equivalence relation.
    36 (iii) (b)
    Verify if any function f:B→Af : B \to A is bijective. Give reason to support your answer.

  3. Question 3

    Relations and Functions. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    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) : A function f:N→Nf : N \to N given by f(x)=x3+2f(x) = x^3 + 2, ∀ x∈N\forall\, x \in N is one-one but not onto. Reason (R) : Since ∀ y∈N\forall\, y \in N (Codomain), there does not exist x=(y−2)1/3x = (y - 2)^{1/3} in N (Domain) such that f(x)=x3+2=yf(x) = x^3 + 2 = y.

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  4. Question 4

    Three Dimensional Geometry. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    9
    The length of perpendicular drawn from the point (1, 2, 3) on line x0=y1=z0\frac{x}{0} = \frac{y}{1} = \frac{z}{0} is

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  5. Question 5

    Three Dimensional Geometry. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    25
    Find the angle between the following pair of lines : x−23=y+52=1−z−6\dfrac{x - 2}{3} = \dfrac{y + 5}{2} = \dfrac{1 - z}{-6} and x−71=y2=6−z−2\dfrac{x - 7}{1} = \dfrac{y}{2} = \dfrac{6 - z}{-2}