PYQ Vault

Day 55: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. This type asked 2 times: 2023, 2026. This one: 2026

    15
    If ∣a⃗∣=8\left| \vec{a} \right| = 8, ∣b⃗∣=3\left| \vec{b} \right| = 3 and ∣a⃗×b⃗∣=12\left| \vec{a} \times \vec{b} \right| = 12, then the value of ∣a⃗⋅b⃗∣\left| \vec{a} \cdot \vec{b} \right|

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. This type asked 2 times: 2023, 2026. This one: 2026

    25 (b)
    A unit vector a⃗\vec{a} is such that it makes an angle π4\dfrac{\pi}{4} with x-axis, π3\dfrac{\pi}{3} with y-axis and an acute angle θ\theta with z-axis. Find θ\theta and the components of a⃗\vec{a}.

  3. Question 3

    Vector Algebra. This type asked 2 times: 2023, 2026. This one: 2026

    24
    If (2i^+3j^+k^)(2\hat{i} + 3\hat{j} + \hat{k}) and (2i^+j^−k^)(2\hat{i} + \hat{j} - \hat{k}) represent the sides AB→\overrightarrow{AB} and AC→\overrightarrow{AC} respectively of Δ\Delta ABC, find the vector representing the median through A.

  4. Question 4

    Application of Derivatives. This type asked 2 times: 2023, 2025. This one: 2025

    29
    Amongst all pairs of positive integers with product as 289, find which of the two numbers add up to the least.

  5. Question 5

    Application of Derivatives. This type asked 2 times: 2024, 2025. This one: 2025

    29
    Show that of all the rectangles with a fixed perimeter, the square has the greatest area.