PYQ Vault

Day 277: CBSE Class 12 Maths

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

  1. Question 1

    Relations and Functions. Asked once: 2026

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : A relation R on the set {1, 2, 3}\{1,\ 2,\ 3\} defined as R={(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}R = \{(1,\ 1),\ (1,\ 2),\ (2,\ 1),\ (2,\ 2),\ (3,\ 3)\} is an equivalence relation. Reason (R) : A relation that is reflexive, symmetric and transitive is an equivalence relation.

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  2. Question 2

    Three Dimensional Geometry. Asked once: 2024

    14
    A vector perpendicular to the line r⃗=i^+j^−k^+λ(3i^−j^)\vec{r} = \hat{i} + \hat{j} - \hat{k} + \lambda(3\hat{i} - \hat{j}) is :

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  3. Question 3

    Vector Algebra. Asked once: 2026

    16
    If position vector p⃗\vec{p} of a point (24, n) is such that ∣p⃗∣=25|\vec{p}| = 25, then the value of n is :

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  4. Question 4

    Application of Derivatives. Asked once: 2025

    25
    A cylindrical water container has developed a leak at the bottom. The water is leaking at the rate of 5 cm3/s5\ \text{cm}^3/\text{s} from the leak. If the radius of the container is 15 cm, find the rate at which the height of water is decreasing inside the container, when the height of water is 2 metres.
  5. Question 5

    Determinants. Asked once: 2024

    7
    Let f(x)=∣x2sin⁡xp−1∣\mathrm{f}(x) = \begin{vmatrix} x^2 & \sin x \\ \mathrm{p} & -1 \end{vmatrix}, where p is a constant. The value of p for which f′(0)=1\mathrm{f}'(0) = 1 is :

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