PYQ Vault

Day 11: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    35 (a)
    Find the foot of the perpendicular from the point (0, 2, 3) on the line −x−3−5=1−y−2=3z+129\dfrac{-x - 3}{-5} = \dfrac{1 - y}{-2} = \dfrac{3z + 12}{9} and hence find the length of the perpendicular.

  2. Question 2

    Three Dimensional Geometry. Asked 2 times: 2025, 2026

    33
    Prove that the line through points A(0, -1, -1) and B(4, 5, 1) intersects the line through points C(3, 9, 4) and D(-4, 4, 4). Hence, write the equation of line passing through the point of intersection of lines AB and CD as well as origin.

  3. Question 3

    Three Dimensional Geometry. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    35
    Find the vector and cartesian equations of the line passing through the point of intersection of the lines r⃗=(i^+j^−k^)+λ(3i^−j^)\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) and r⃗=(4i^−k^)+μ(2i^+3k^)\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) and parallel to the line x−1−2=7−y−3=z\dfrac{x - 1}{-2} = \dfrac{7 - y}{-3} = z.

  4. Question 4

    Three Dimensional Geometry. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    35 (b)
    Opposite sides of a square are along the lines : r⃗=i^+2j^−4k^+λ(2i^+3j^+6k^)\vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}) r⃗=3i^+3j^−5k^+μ(2i^+3j^+6k^)\vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) Find the area of the square if direction ratios of other pair of opposite sides of the square are given by <−3,6,p><-3, 6, p>. Also, find the value of p.

  5. Question 5

    Vector Algebra. Asked 2 times: 2022*, 2026 (* = numbers or wording changed that year)

    24 (a)
    Three honey bees were found flying along the vectors a⃗=2i^−3j^+k^\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}, b⃗=4j^−2k^\vec{b} = 4\hat{j} - 2\hat{k} and c⃗=3i^+2k^\vec{c} = 3\hat{i} + 2\hat{k} respectively. Find the value of λ\lambda such that the path for a⃗+λb⃗\vec{a} + \lambda \vec{b} is perpendicular to c⃗\vec{c}.