PYQ Vault

Day 276: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Vector Algebra. Asked once: 2026

    30 (a)
    Let three toys A, B and C be placed in the same straight line. If the position vectors of A, B and C are 55i^−2j^55\hat{i} - 2\hat{j}, 5i^+8j^5\hat{i} + 8\hat{j} and ai^−52j^a\hat{i} - 52\hat{j} respectively, find the value of ‘a’.

  2. Question 2

    Application of Derivatives. Asked once: 2025

    22
    Let the volume of a metallic hollow sphere be constant. If the inner radius increases at the rate of 2 cm/s, find the rate of increase of the outer radius when the radii are 2 cm and 4 cm respectively.

  3. Question 3

    Determinants. Asked once: 2024

    4
    If A=[aij]=[2−15132504]A = [a_{ij}] = \begin{bmatrix} 2 & -1 & 5 \\ 1 & 3 & 2 \\ 5 & 0 & 4 \end{bmatrix} and cijc_{ij} is the cofactor of element aija_{ij}, then the value of a21⋅c11+a22⋅c12+a23⋅c13a_{21} \cdot c_{11} + a_{22} \cdot c_{12} + a_{23} \cdot c_{13} is :

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  4. Question 4

    Integrals. Asked once: 2025

    31
    f and g are continuous functions on interval [a, b]. Given that f(a−x)=f(x)f(a - x) = f(x) and g(x)+g(a−x)=ag(x) + g(a - x) = a, show that ∫0af(x) g(x) dx=a2∫0af(x) dx\displaystyle\int_0^{a} f(x)\,g(x)\,dx = \dfrac{a}{2} \displaystyle\int_0^{a} f(x)\,dx.

  5. Question 5

    Matrices. Asked once: 2026

    13
    Which of the following cannot be an order of a column-matrix ?

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