PYQ Vault

Day 143: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2023 (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) : If a line makes angles α,β,γ\alpha, \beta, \gamma with positive direction of the coordinate axes, then sin⁡2α+sin⁡2β+sin⁡2γ=2\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 2. Reason (R) : The sum of squares of the direction cosines of a line is 1.

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  2. Question 2

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    9
    If the point P(a, b, 0) lies on the line x+12=y+23=z+34\frac{x+1}{2} = \frac{y+2}{3} = \frac{z+3}{4}, then (a, b) is :

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  3. Question 3

    Vector Algebra. Asked once: 2023 (same type asked 4 times)

    24 (b)
    Find the area of a parallelogram whose adjacent sides are determined by the vectors a⃗=i^−j^+3k^\vec{a} = \hat{i} - \hat{j} + 3\hat{k} and b⃗=2i^−7j^+k^\vec{b} = 2\hat{i} - 7\hat{j} + \hat{k}.

  4. Question 4

    Vector Algebra. Asked once: 2023 (same type asked 4 times)

    18
    For what value of λ\lambda, the projection of vector i^+λj^\hat{i} + \lambda\hat{j} on vector i^−j^\hat{i} - \hat{j} is 2\sqrt{2} ?

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  5. Question 5

    Vector Algebra. Asked once: 2025 (same type asked 4 times)

    1
    If p⃗\vec{p} and q⃗\vec{q} are unit vectors, then which of the following values of p⃗⋅q⃗\vec{p} \cdot \vec{q} is not possible ?

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