PYQ Vault

Day 128: 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 2 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) : Equation of a line passing through the points (1, 2, 3) and (3,−1,3)(3, -1, 3) is x−32=y+13=z−30\frac{x - 3}{2} = \frac{y + 1}{3} = \frac{z - 3}{0}. Reason (R) : Equation of a line passing through points (x1,y1,z1)(x_1, y_1, z_1), (x2,y2,z2)(x_2, y_2, z_2) is given by x−x1x2−x1=y−y1y2−y1=z−z1z2−z1\frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2 - z_1}.

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  2. Question 2

    Vector Algebra. Asked once: 2026 (same type asked 2 times)

    24
    Using vectors, find the area of ΔABC\Delta ABC with vertices A(1, 2, 3), B(2, -1, 4) and C(4, 5, -1).

  3. Question 3

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    1
    If the angle between a⃗\vec{a} and b⃗\vec{b} is π3\frac{\pi}{3} and ∣a⃗×b⃗∣=33|\vec{a} \times \vec{b}| = 3\sqrt{3}, then the value of a⃗⋅b⃗\vec{a} \cdot \vec{b} is

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  4. Question 4

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    6
    The direction cosines of vector BA→\overrightarrow{BA}, where coordinates of A and B are (1,2,−1)(1, 2, -1) and (3, 4, 0) respectively, are :

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  5. Question 5

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    12
    In Δ ABC\Delta \, ABC, AB→=i^+j^+2k^\overrightarrow{AB} = \hat{i} + \hat{j} + 2\hat{k} and AC→=3i^−j^+4k^\overrightarrow{AC} = 3\hat{i} - \hat{j} + 4\hat{k}. If D is mid-point of BC, then vector AD→\overrightarrow{AD} is equal to :

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