PYQ Vault

Day 283: CBSE Class 12 Maths

5 questions (11 parts). Try each one first, then open its answer.

  1. Question 1

    Relations and Functions. Asked once: 2025

    26 (b)
    Let A={1,2,3}A = \{1, 2, 3\} and B={4,5,6}B = \{4, 5, 6\}. A relation R from A to B is defined as R={(x,y):x+y=6,x∈A,y∈B}R = \{(x, y) : x + y = 6, x \in A, y \in B\}. (i) Write all elements of R. (ii) Is R a function ? Justify. (iii) Determine domain and range of R.

  2. Question 2

    Vector Algebra. Asked once: 2024

    25
    Let a⃗\vec{a} and b⃗\vec{b} be two non-zero vectors. Prove that ∣a⃗×b⃗∣≤∣a⃗∣∣b⃗∣|\vec{a} \times \vec{b}| \le |\vec{a}||\vec{b}|. State the condition under which equality holds, i.e., ∣a⃗×b⃗∣=∣a⃗∣∣b⃗∣|\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|.

  3. Question 3

    Relations and Functions. Asked once: 2024

    14
    Which of the following statements is not true about equivalence classes AiA_i (i = 1, 2, .... n) formed by an equivalence relation R defined on a set A ?

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  4. Question 4 (case study, 4 parts)

    Vector Algebra. Asked once: 2024

    An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors 2i^+3j^+4k^2\hat{i} + 3\hat{j} + 4\hat{k}, 7i^+5j^+8k^7\hat{i} + 5\hat{j} + 8\hat{k} and −3i^+7j^+11k^-3\hat{i} + 7\hat{j} + 11\hat{k} respectively. Based on the above information, answer the following questions :
    37 (i)
    How far is the star V from star A ?
    37 (ii)
    Find a unit vector in the direction of DA→\overrightarrow{DA}.
    37 (iii) (a)
    Find the measure of ∠VDA\angle VDA.
    37 (iii) (b)
    What is the projection of vector DV→\overrightarrow{DV} on vector DA→\overrightarrow{DA} ?

  5. Question 5 (case study, 4 parts)

    Relations and Functions. Asked once: 2024

    Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by R = {(l1,l2):l1\{(l_1, l_2) : l_1 is parallel to l2}l_2\} On the basis of the above information, answer the following questions :
    36 (a) (i)
    Find whether the relation R is symmetric or not.
    36 (a) (ii)
    Find whether the relation R is transitive or not.
    36 (a) (iii)
    If one of the rail lines on the railway track is represented by the equation y=3x+2\mathrm{y} = 3x + 2, then find the set of rail lines in R related to it.
    36 (b)
    Let S be the relation defined by S = {(l1,l2):l1\{(l_1, l_2) : l_1 is perpendicular to l2}l_2\} check whether the relation S is symmetric and transitive.