PYQ Vault

Day 279: CBSE Class 12 Maths

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

  1. Question 1

    Determinants. Asked once: 2024

    6
    If aija_{ij} and AijA_{ij} represent the (ij)th(ij)^{th} element and its cofactor of [2−3560415−7]\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} respectively, then the value of a11A21+a12A22+a13A23a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} is :

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  2. Question 2

    Integrals. Asked once: 2022

    12
    Evaluate : ∫01x(1−x)n dx\int_{0}^{1} x (1 - x)^n \, dx

  3. Question 3

    Matrices. Asked once: 2024

    1
    If A=[aij]A = [a_{ij}] is an identity matrix, then which of the following is true ?

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  4. Question 4 (case study, 4 parts)

    Relations and Functions. Asked once: 2025

    A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set A = {1, 2, 3} : R1={(2,3),(3,2)}R_1 = \{(2, 3), (3, 2)\} R2={(1,2),(1,3),(3,2)}R_2 = \{(1, 2), (1, 3), (3, 2)\} R3={(1,2),(2,1),(1,1)}R_3 = \{(1, 2), (2, 1), (1, 1)\} R4={(1,1),(1,2),(3,3),(2,2)}R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\} R5={(1,1),(1,2),(3,3),(2,2),(2,1),(2,3),(3,2)}R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\} The students are asked to answer the following questions about the above relations :
    37 (i)
    Identify the relation which is reflexive, transitive but not symmetric.
    37 (ii)
    Identify the relation which is reflexive and symmetric but not transitive.
    37 (iii) (a)
    Identify the relations which are symmetric but neither reflexive nor transitive.
    37 (iii) (b)
    What pairs should be added to the relation R2R_2 to make it an equivalence relation ?

  5. Question 5

    Vector Algebra. Asked once: 2025

    31 (a)
    The scalar product of the vector a⃗=i^−j^+2k^\vec{a} = \hat{i} - \hat{j} + 2\hat{k} with a unit vector along sum of vectors b⃗=2i^−4j^+5k^\vec{b} = 2\hat{i} - 4\hat{j} + 5\hat{k} and c⃗=λi^−2j^−3k^\vec{c} = \lambda\hat{i} - 2\hat{j} - 3\hat{k} is equal to 1. Find the value of λ\lambda.