PYQ Vault

Day 194: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2022 (same type asked 4 times)

    6
    There are two bags. Bag I contains 1 red and 3 white balls, and Bag II contains 3 red and 5 white balls. A bag is selected at random and a ball is drawn from it. Find the probability that the ball so drawn is red in colour.

  2. Question 2

    Probability. Asked once: 2022 (same type asked 4 times)

    4
    A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the probability that the number appearing on at least one die is 3.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2025 (same type asked 4 times)

    35 (a)
    Find the foot of the perpendicular drawn from the point (1,1,4)(1, 1, 4) on the line x+25=y+12=−z+4−3\dfrac{x+2}{5} = \dfrac{y+1}{2} = \dfrac{-z+4}{-3}.

  4. Question 4

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    34 (b)
    Find the equations of the line passing through the points A(1, 2, 3) and B(3, 5, 9). Hence, find the coordinates of the points on this line which are at a distance of 14 units from point B.

  5. Question 5 (case study, 2 parts)

    Three Dimensional Geometry. Asked once: 2022 (same type asked 4 times)

    Two motorcycles A and B are running at the speed more than the allowed speed on the roads represented by the lines r⃗=λ(i^+2j^−k^)\vec{r} = \lambda\left(\hat{i} + 2\hat{j} - \hat{k}\right) and r⃗=(3i^+3j^)+μ(2i^+j^+k^)\vec{r} = \left(3\hat{i} + 3\hat{j}\right) + \mu\left(2\hat{i} + \hat{j} + \hat{k}\right) respectively. Based on the above information, answer the following questions :
    14 (a)
    Find the shortest distance between the given lines.
    14 (b)
    Find the point at which the motorcycles may collide.