PYQ Vault

Day 44: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. This type asked 3 times: 2022, 2023, 2026. This one: 2026

    13
    The value of p for which vectors i^+2j^+3k^\hat{i} + 2\hat{j} + 3\hat{k} and 2i^−pj^+k^2\hat{i} - p\hat{j} + \hat{k} are perpendicular to each other is

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  2. Question 2

    Vector Algebra. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    16
    If (3i^−2j^+5k^)×(4i^+pj^+qk^)=0⃗(3\hat{i} - 2\hat{j} + 5\hat{k}) \times (4\hat{i} + p\hat{j} + q\hat{k}) = \vec{0}, then the values of p and q are :

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  3. Question 3

    Vector Algebra. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    23
    Find the vector of magnitude 14 in the direction of QP→\overrightarrow{QP}, where P and Q are the points (1, 3, 2) and (-1, 0, 8) respectively.

  4. Question 4

    Vector Algebra. This type asked 3 times: 2022, 2024, 2026. This one: 2026

    30 (b)
    If a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} are unit vectors, then prove that ∣a⃗−b⃗∣2+∣b⃗−c⃗∣2+∣c⃗−a⃗∣2≤9|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \le 9.

  5. Question 5

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    25
    Find the local maxima and local minima of the function f(x)=83x3−12x2+18x+5f(x) = \frac{8}{3}x^3 - 12x^2 + 18x + 5.