PYQ Vault

Day 118: CBSE Class 12 Maths

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

  1. Question 1 (case study, 4 parts)

    Relations and Functions. Asked once: 2023 (same type asked 3 times)

    An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3}\{b_1, b_2, b_3\} and G = {g1,g2}\{g_1, g_2\}, where B represents the set of Boys selected and G the set of Girls selected for the final race. Based on the above information, answer the following questions :
    36 (i)
    How many relations are possible from B to G ?
    36 (ii)
    Among all the possible relations from B to G, how many functions can be formed from B to G ?
    36 (iii) (a)
    Let R:B→BR : B \to B be defined by R={(x,y):x and y are students of the same sex}R = \{(x, y) : x \text{ and } y \text{ are students of the same sex}\}. Check if R is an equivalence relation.
    36 (iii) (b)
    A function f:B→Gf : B \to G be defined by f={(b1,g1),(b2,g2),(b3,g1)}f = \{(b_1, g_1), (b_2, g_2), (b_3, g_1)\}. Check if f is bijective. Justify your answer.

  2. Question 2

    Relations and Functions. Asked once: 2023 (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.
    20
    Assertion (A) : The number of onto functions from a set P containing 5 elements to a set Q containing 2 elements is 30. Reason (R) : Number of onto functions from a set containing m elements to a set containing n elements is nmn^m.

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  3. Question 3

    Three Dimensional Geometry. Asked once: 2026 (same type asked 3 times)

    16
    The length of perpendicular drawn from point (2, 5, 7) on line x1=y0=z0\frac{x}{1} = \frac{y}{0} = \frac{z}{0} is

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2023 (same type asked 3 times)

    16
    The angle between the lines 2x=3y=−z2x = 3y = -z and 6x=−y=−4z6x = -y = -4z is

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  5. Question 5

    Vector Algebra. Asked once: 2023 (same type asked 3 times)

    8
    The value of p for which the vectors 2i^+pj^+k^2\hat{i} + p\hat{j} + \hat{k} and −4i^−6j^+26k^-4\hat{i} - 6\hat{j} + 26\hat{k} are perpendicular to each other, is :

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