PYQ Vault

Day 33: CBSE Class 12 Maths

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

  1. Question 1

    Probability. This type asked 4 times: 2022, 2023, 2025, 2026. This one: 2026

    31 (b)
    A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let A be the event of getting sum of the numbers on two cards as 10, and B, the event of a number other than 4 on the first card selected. Find P(A and B) and find whether the events A and B are independent events or not.

  2. Question 2

    Three Dimensional Geometry. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    35
    Find the length of the perpendicular drawn from the point P(1, 2, 3) to the line x−63=y−72=z−7−2\dfrac{x - 6}{3} = \dfrac{y - 7}{2} = \dfrac{z - 7}{-2}. Also, find the equation of the perpendicular line joining P and the foot of the perpendicular.

  3. Question 3

    Three Dimensional Geometry. This type asked 4 times: 2022, 2023, 2025, 2026. This one: 2026

    30 (a)
    Find a point on the line x−23=1−y2=z−32\dfrac{x - 2}{3} = \dfrac{1 - y}{2} = \dfrac{z - 3}{2} at a distance of 2\sqrt{2} units from the point (1, 2, 3).

  4. Question 4

    Three Dimensional Geometry. This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026

    30 (b)
    Find the shortest distance between the lines r⃗=(4+λ)i^+(2λ−1)j^−3λk^\vec{r} = (4 + \lambda)\hat{i} + (2\lambda - 1)\hat{j} - 3\lambda\hat{k} r⃗=(1+2μ)i^+(2−5μ)k^+(4μ−1)j^\vec{r} = (1 + 2\mu)\hat{i} + (2 - 5\mu)\hat{k} + (4\mu - 1)\hat{j}.

  5. Question 5

    Three Dimensional Geometry. This type asked 4 times: 2022, 2023, 2024, 2026. This one: 2026

    35 (a)
    Represent the equations of lines l1l_1 and l2l_2 in vector form and check whether they are intersecting or not. l1:x+3−3=y−11=z−55l_1 : \dfrac{x + 3}{-3} = \dfrac{y - 1}{1} = \dfrac{z - 5}{5} l2:x+1−1=2−y−2=z−55l_2 : \dfrac{x + 1}{-1} = \dfrac{2 - y}{-2} = \dfrac{z - 5}{5}