PYQ Vault

Day 12: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    15
    If (a⃗+b⃗)⋅(a⃗−b⃗)=198(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 198 and ∣a⃗∣=10∣b⃗∣|\vec{a}| = 10|\vec{b}|, then :

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked 2 times: 2022*, 2026 (* = numbers or wording changed that year)

    24
    If for two unit vectors a⃗\vec{a} and b⃗\vec{b}, ∣a⃗+2b⃗∣=∣2a⃗−b⃗∣|\vec{a} + 2\vec{b}| = |2\vec{a} - \vec{b}|, then find the angle between a⃗\vec{a} and b⃗\vec{b}.

  3. Question 3

    Vector Algebra. Asked 2 times: 2025, 2026

    24
    If AB→=j^+k^\overrightarrow{AB} = \hat{j} + \hat{k} and AC→=3i^−j^+4k^\overrightarrow{AC} = 3\hat{i} - \hat{j} + 4\hat{k} represent the two vectors along the sides AB and AC of ΔABC\Delta ABC, prove that the median AD→=AB→+AC→2\overrightarrow{AD} = \dfrac{\overrightarrow{AB} + \overrightarrow{AC}}{2}, where D is midpoint of BC. Hence, find the length of median AD.

  4. Question 4

    Vector Algebra. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    24
    If the position vectors of three points A, B and C are 3i^+j^3\hat{i} + \hat{j}, 5i^+6j^−3k^5\hat{i} + 6\hat{j} - 3\hat{k} and 4j^4\hat{j} respectively, then show that they form an isosceles triangle.

  5. Question 5

    Vector Algebra. Asked 2 times: 2022, 2026

    14
    The value of m for which the points with position vectors −i^−j^+2k^-\hat{i} - \hat{j} + 2\hat{k}, 2i^+mj^+5k^2\hat{i} + m\hat{j} + 5\hat{k} and 3i^+11j^+6k^3\hat{i} + 11\hat{j} + 6\hat{k} are collinear, is

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