PYQ Vault

Day 86: CBSE Class 12 Maths

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

  1. Question 1

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

    35 (b)
    A box contains 10 tickets, 2 of which carry a prize of ₹ 8 each, 5 of which carry a prize of ₹ 4 each, and remaining 3 carry a prize of ₹ 2 each. If one ticket is drawn at random, find the mean value of the prize.

  2. Question 2

    Relations and Functions. Asked once: 2025 (same type asked 3 times)

    26 (a)
    If f:R+→Rf : R^+ \to R is defined as f(x)=log⁡axf(x) = \log_a x (a>0(a > 0 and a≠1)a \ne 1), prove that f is a bijection. (R+R^+ is a set of all positive real numbers.)

  3. Question 3

    Relations and Functions. Asked once: 2025 (same type asked 3 times)

    26 (b)
    Let R be a relation defined on a set N of natural numbers such that R={(x,y):xy is a square of a natural number, x, y∈N}R = \{(x, y) : xy \text{ is a square of a natural number},\ x,\ y \in N\}. Determine if the relation R is an equivalence relation.

  4. Question 4

    Vector Algebra. Asked once: 2025 (same type asked 3 times)

    1
    The values of xx for which the angle between the vectors a⃗=2x2i^+4xj^+k^\vec{a} = 2x^2\hat{i} + 4x\hat{j} + \hat{k} and b⃗=7i^−2j^+xk^\vec{b} = 7\hat{i} - 2\hat{j} + x\hat{k} is obtuse, is :

    Tap an option to check your answer.

  5. Question 5

    Vector Algebra. Asked once: 2025 (same type asked 3 times)

    21 (b)
    If α⃗\vec{\alpha} and β⃗\vec{\beta} are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that QR=32QPQR = \dfrac{3}{2} QP.