PYQ Vault

Day 72: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2024 (same type asked 4 times)

    9
    If α\alpha, β\beta and γ\gamma are the angles which a line makes with positive directions of x, y and z axes respectively, then which of the following is not true ?

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  2. Question 2

    Three Dimensional Geometry. Asked once: 2026 (same type asked 4 times)

    25
    Find the co-ordinates of the point on the line r⃗=−j^+3k^+λ(2i^−2j^+k^)\vec{r} = -\hat{j} + 3\hat{k} + \lambda(2\hat{i} - 2\hat{j} + \hat{k}) such that the sum of co-ordinates is 3.

  3. Question 3

    Vector Algebra. Asked once: 2026 (same type asked 4 times)

    24
    If in a parallelogram PQRS, PQ→=2i^+3j^+k^\overrightarrow{PQ} = 2\hat{i} + 3\hat{j} + \hat{k} and QR→=i^−2j^+k^\overrightarrow{QR} = \hat{i} - 2\hat{j} + \hat{k}, then find the unit vectors parallel to the diagonals PR→\overrightarrow{PR} and SQ→\overrightarrow{SQ}.

  4. Question 4

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

    1
    The projection vector of vector a⃗\vec{a} on vector b⃗\vec{b} is

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  5. Question 5

    Vector Algebra. Asked once: 2026 (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.
    19
    For two vectors a⃗\vec{a} and b⃗\vec{b} Assertion (A) : ∣a⃗×b⃗∣2+(a⃗⋅b⃗)2=∣a⃗∣2∣b⃗∣2|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2 |\vec{b}|^2 Reason (R) : ∣a⃗×b⃗∣=(a⃗⋅b⃗)tan⁡θ|\vec{a} \times \vec{b}| = (\vec{a} \cdot \vec{b}) \tan \theta, (θ≠π2)\left(\theta \neq \dfrac{\pi}{2}\right)

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