PYQ Vault

Day 282: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2023

    24
    Find the points on the curve 6y=x3+26y = x^3 + 2 at which ordinate is changing 8 times as fast as abscissa.

  2. Question 2

    Relations and Functions. Asked once: 2025

    27
    Prove that f:N→Nf : N \rightarrow N defined as f(x)=ax+bf(x) = ax + b (a,b∈N)(a, b \in N) is one-one but not onto.

  3. Question 3

    Vector Algebra. Asked once: 2025

    24
    If ∣a⃗∣=2|\vec{a}| = 2, ∣b⃗∣=3|\vec{b}| = 3 and a⃗⋅b⃗=4\vec{a} \cdot \vec{b} = 4, then evaluate ∣a⃗+2b⃗∣|\vec{a} + 2\vec{b}|.

  4. Question 4

    Relations and Functions. Asked once: 2025

    28 (b)
    Show that the function f:N→Nf : N \to N, where N is a set of natural numbers, given by f(n)={n−1,if n is evenn+1,if n is oddf(n) = \begin{cases} n - 1, & \text{if } n \text{ is even} \\ n + 1, & \text{if } n \text{ is odd} \end{cases} is a bijection.

  5. Question 5

    Vector Algebra. Asked once: 2025

    24
    Let p⃗=2i^−3j^−k^\vec{p} = 2\hat{i} - 3\hat{j} - \hat{k}, q⃗=−3i^+4j^+k^\vec{q} = -3\hat{i} + 4\hat{j} + \hat{k} and r⃗=i^+j^+2k^\vec{r} = \hat{i} + \hat{j} + 2\hat{k}. Express r⃗\vec{r} in the form of r⃗=λp⃗+μq⃗\vec{r} = \lambda\vec{p} + \mu\vec{q} and hence find the values of λ\lambda and μ\mu.