PYQ Vault

Day 212: CBSE Class 12 Maths

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

  1. Question 1

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

    6 (a)
    A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.

  2. Question 2

    Three Dimensional Geometry. Asked once: 2024 (same type asked 4 times)

    34 (a)
    Find the co-ordinates of the foot of the perpendicular drawn from the point (2,3,−8)(2, 3, -8) to the line 4−x2=y6=1−z3\dfrac{4 - x}{2} = \dfrac{\mathrm{y}}{6} = \dfrac{1 - \mathrm{z}}{3}. Also, find the perpendicular distance of the given point from the line.

  3. Question 3

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

    10
    Find the co-ordinates of the point on the line x+23=y+12=z−32\frac{x + 2}{3} = \frac{y + 1}{2} = \frac{z - 3}{2} which is at a distance of 5 units from the point (1,3,3)(1, 3, 3).

  4. Question 4

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

    7
    Find the shortest distance between the following lines : r⃗=3i^+5j^+7k^+λ(i^−2j^+k^)\vec{r} = 3\hat{i} + 5\hat{j} + 7\hat{k} + \lambda(\hat{i} - 2\hat{j} + \hat{k}) and r⃗=(−i^−j^−k^)+μ(7i^−6j^+k^)\vec{r} = (-\hat{i} - \hat{j} - \hat{k}) + \mu(7\hat{i} - 6\hat{j} + \hat{k}).

  5. Question 5

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

    23 (b)
    Check whether the lines given by equations x=2λ+2x = 2\lambda + 2, y=7λ+1y = 7\lambda + 1, z=−3λ−3z = -3\lambda - 3 and x=−μ−2x = -\mu - 2, y=2μ+8y = 2\mu + 8, z=4μ+5z = 4\mu + 5 are perpendicular to each other or not.