PYQ Vault

Day 119: CBSE Class 12 Maths

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

  1. Question 1

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

    24
    If a⃗\vec{a} and b⃗\vec{b} are two non-collinear vectors, then find xx, such that α⃗=(x−2) a⃗+b⃗\vec{\alpha} = (x - 2)\,\vec{a} + \vec{b} and β⃗=(3+2x) a⃗−2b⃗\vec{\beta} = (3 + 2x)\,\vec{a} - 2\vec{b} are collinear.

  2. Question 2

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

    8
    Unit vector along PQ→\overrightarrow{PQ}, where coordinates of P and Q respectively are (2, 1, −1-1) and (4, 4, −7-7), is

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  3. Question 3

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

    10
    If a⃗\vec{a} and b⃗\vec{b} are two vectors of equal magnitude and α\alpha is the angle between them, then prove that ∣a⃗+b⃗∣∣a⃗−b⃗∣=cot⁡(α2)\dfrac{|\vec{a} + \vec{b}|}{|\vec{a} - \vec{b}|} = \cot\left(\dfrac{\alpha}{2}\right).

  4. Question 4

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    10
    The slope of the curve y=−x3+3x2+8x−20y = -x^3 + 3x^2 + 8x - 20 is maximum at :

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  5. Question 5

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    13
    If f(x)=2x+cos⁡xf(x) = 2x + \cos x, then f(x) :

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