PYQ Vault

Day 71: CBSE Class 12 Maths

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

  1. Question 1

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

    35 (b)
    Find the point on the line x−13=y+12=z−43\dfrac{x-1}{3} = \dfrac{y+1}{2} = \dfrac{z-4}{3} at a distance of 222\sqrt{2} units from the point (−1,−1,2)(-1, -1, 2).

  2. Question 2

    Three Dimensional Geometry. Asked once: 2026 (same type asked 4 times)

    35 (b)
    Find the value of p if the shortest distance between the lines r⃗=(i^+2j^+k^)+λ(i^−j^+k^)\vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) and r⃗=(pi^−j^−k^)+μ(2i^+j^+2k^)\vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) is 32\dfrac{3}{\sqrt{2}} units.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2026 (same type asked 4 times)

    35
    A line passing through the points A(1, 2, 3) and B(5, 8, 11) intersects the line r⃗=4i^+j^+λ(5i^+2j^+k^)\vec{r} = 4\hat{i} + \hat{j} + \lambda(5\hat{i} + 2\hat{j} + \hat{k}). Find the co-ordinates of the point of intersection. Hence, write the equation of a line passing through the point of intersection and perpendicular to both the lines.

  4. Question 4

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

    25
    Find the value of λ\lambda if the following lines are perpendicular to each other : l1:1−x−3=3y−22λ=z−33l_1 : \dfrac{1 - x}{-3} = \dfrac{3y - 2}{2\lambda} = \dfrac{z - 3}{3} l2:x−13λ=1−y1=2z−53l_2 : \dfrac{x - 1}{3\lambda} = \dfrac{1 - y}{1} = \dfrac{2z - 5}{3}

  5. Question 5

    Three Dimensional Geometry. Asked once: 2026 (same type asked 4 times)

    15
    Direction cosines of the line given by equations : 2x−14=1−y3=−z6\dfrac{2x - 1}{4} = \dfrac{1 - y}{3} = \dfrac{-z}{6} are

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