PYQ Vault

Day 286: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2024

    7
    Let θ\theta be the angle between two unit vectors a^\hat{a} and b^\hat{b} such that sin⁡θ=35\sin \theta = \frac{3}{5}. Then, a^⋅b^\hat{a} \cdot \hat{b} is equal to :

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  2. Question 2

    Relations and Functions. Asked once: 2023

    1
    Let R be a relation in the set N given by R={(a,b):a=b−2,b>6}R = \{(a, b) : a = b - 2, b > 6\}. Then

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  3. Question 3

    Vector Algebra. Asked once: 2023

    28 (b)
    If a⃗=i^+j^+k^\vec{a} = \hat{i} + \hat{j} + \hat{k} and b⃗=i^+2j^+3k^\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} then find a unit vector perpendicular to both a⃗+b⃗\vec{a} + \vec{b} and a⃗−b⃗\vec{a} - \vec{b}.

  4. Question 4

    Vector Algebra. Asked once: 2023

    23
    If a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} are three non-zero unequal vectors such that a⃗⋅b⃗=a⃗⋅c⃗\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c}, then find the angle between a⃗\vec{a} and b⃗−c⃗\vec{b} - \vec{c}.

  5. Question 5

    Vector Algebra. Asked once: 2023

    2
    The position vectors of three consecutive vertices of a parallelogram ABCD are A (4i^+2j^−6k^)(4\hat{i} + 2\hat{j} - 6\hat{k}), B (5i^−3j^+k^)(5\hat{i} - 3\hat{j} + \hat{k}) and C (12i^+4j^+5k^)(12\hat{i} + 4\hat{j} + 5\hat{k}). The position vector of D is given by

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