PYQ Vault

Day 218: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Continuity and Differentiability. Asked once: 2023 (same type asked 3 times)

    The equation of the path traced by a roller-coaster is given by the polynomial f(x)=a(x+9)(x+1)(x−3)f(x) = a(x + 9)(x + 1)(x - 3). If the roller-coaster crosses y-axis at a point (0,−1)(0, -1), answer the following :
    38 (i)
    Find the value of 'a'.
    38 (ii)
    Find f′′(x)f''(x) at x = 1.

  2. Question 2

    Determinants. Asked once: 2024 (same type asked 3 times)

    2
    If A is a square matrix of order 2 and ∣A∣=−2\left|\mathrm{A}\right| = -2, then value of ∣5A′∣\left|5\mathrm{A}'\right| is :

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  3. Question 3

    Integrals. Asked once: 2024 (same type asked 3 times)

    12
    If g(x)g(x) is a continuous function satisfying g(−x)=−g(x)g(-x) = -g(x), then ∫02ag(x) dx\int\limits_{0}^{2a} g(x)\, dx is equal to :

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  4. Question 4

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

    27
    Find ∫ecot⁡−1x(1−x+x21+x2)dx\int e^{\cot^{-1} x}\left(\frac{1 - x + x^2}{1 + x^2}\right) dx.

  5. Question 5

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

    1
    If ddxf(x)=2x+3x\frac{d}{dx} f(x) = 2x + \frac{3}{x} and f(1)=1f(1) = 1, then f(x)f(x) is

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