PYQ Vault

Day 109: CBSE Class 12 Maths

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

  1. Question 1

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

    35 (b)
    If the lines x−1−3=y−22k=z−32\dfrac{x-1}{-3} = \dfrac{y-2}{2k} = \dfrac{z-3}{2} and x−13k=y−11=z−6−7\dfrac{x-1}{3k} = \dfrac{y-1}{1} = \dfrac{z-6}{-7} are perpendicular to each other, find the value of k and hence write the vector equation of a line perpendicular to these two lines and passing through the point (3,−4,7)(3, -4, 7).

  2. Question 2

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

    1
    Direction cosines of line 1−x0=y=z\dfrac{1 - x}{0} = y = z are

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  3. Question 3

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

    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 in space cannot be drawn perpendicular to x, y and z axes simultaneously. Reason (R) : For any line making angles, α\alpha, β\beta, γ\gamma with the positive directions of x, y and z axes respectively, cos⁡2α+cos⁡2β+cos⁡2γ=1\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1.

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  4. Question 4

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

    13
    The line x=1+5μx = 1 + 5\mu, y=−5+μy = -5 + \mu, z=−6−3μz = -6 - 3\mu passes through which of the following point ?

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  5. Question 5

    Vector Algebra. Asked once: 2024 (same type asked 4 times)

    25
    In the given figure, ABCD is a parallelogram. If AB→=2i^−4j^+5k^\overrightarrow{AB} = 2\hat{i} - 4\hat{j} + 5\hat{k} and DB→=3i^−6j^+2k^\overrightarrow{DB} = 3\hat{i} - 6\hat{j} + 2\hat{k}, then find AD→\overrightarrow{AD} and hence find the area of parallelogram ABCD.