PYQ Vault

Day 34: CBSE Class 12 Maths

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

  1. Question 1

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

    25 (a)
    If the lines x−31=1−y1=z+2p\dfrac{x - 3}{1} = \dfrac{1 - y}{1} = \dfrac{z + 2}{p} and 2−x3=y+15=z+562p\dfrac{2 - x}{3} = \dfrac{y + 1}{5} = \dfrac{z + 56}{2p} are perpendicular to each other, then find the value(s) of p.

  2. Question 2

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

    8
    Direction cosines of line x=y=1−zx = y = 1 - z are

    Tap an option to check your answer.

  3. Question 3

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

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : A line can have direction cosines <1,1,1>< 1, 1, 1 > Reason (R) : cos⁡θ=1\cos \theta = 1 is possible for θ=0\theta = 0.

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  4. Question 4

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

    21
    Find the co-ordinates of the point on line x=y−12=z−23x = \dfrac{y - 1}{2} = \dfrac{z - 2}{3} whose y co-ordinate is 3 times the xx co-ordinate.

  5. Question 5

    Vector Algebra. This type asked 4 times: 2022, 2023, 2024, 2026. This one: 2026

    24
    Vectors a⃗=3i^−2j^+2k^\vec{a} = 3\hat{i} - 2\hat{j} + 2\hat{k} and b⃗=i^+2k^\vec{b} = \hat{i} + 2\hat{k} represent the two adjacent sides of a parallelogram. Find the vectors representing its diagonals and hence find their lengths.