PYQ Vault

Day 151: 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 3 times)

    35 (b)
    Find the angle between the lines 2x=3y=−z2x = 3y = -z and 6x=−y=−4z6x = -y = -4z.

  2. Question 2

    Vector Algebra. Asked once: 2022 (same type asked 3 times)

    6
    If a⃗=2i^+yj^+k^\vec{a} = 2\hat{i} + y\hat{j} + \hat{k} and b⃗=i^+2j^+3k^\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} are two vectors for which the vector (a⃗+b⃗)(\vec{a} + \vec{b}) is perpendicular to the vector (a⃗−b⃗)(\vec{a} - \vec{b}), then find all the possible values of y.

  3. Question 3

    Vector Algebra. Asked once: 2025 (same type asked 3 times)

    15
    A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector 3i^+15j^+6k^3\hat{i} + 15\hat{j} + 6\hat{k} and the other is along the vector 2i^+10j^+λk^2\hat{i} + 10\hat{j} + \lambda\hat{k}, then the value of λ\lambda is :

    Tap an option to check your answer.

  4. Question 4

    Vector Algebra. Asked once: 2023 (same type asked 3 times)

    12
    A unit vector along the vector 4i^−3k^4\hat{i} - 3\hat{k} is :

    Tap an option to check your answer.

  5. Question 5

    Vector Algebra. Asked once: 2022 (same type asked 3 times)

    8 (a)
    If a⃗\vec{a} and b⃗\vec{b} are two vectors such that ∣a⃗+b⃗∣=∣b⃗∣\left|\vec{a} + \vec{b}\right| = \left|\vec{b}\right|, then prove that (a⃗+2b⃗)\left(\vec{a} + 2\vec{b}\right) is perpendicular to a⃗\vec{a}.