PYQ Vault

Day 84: CBSE Class 12 Maths

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

  1. Question 1

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

    9
    The number of arbitrary constants in the particular solution of the differential equation log⁡(dydx)=3x+4y; y(0)=0\log\left(\dfrac{dy}{dx}\right) = 3x + 4y;\ y(0) = 0 is/are

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  2. Question 2

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

    3
    If f(2a−x)=f(x)f(2a - x) = f(x), then ∫02af(x) dx\displaystyle\int_0^{2a} f(x)\,dx is

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  3. Question 3

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

    14
    ∫ex(cos⁡x−sin⁡x) dx\int e^x (\cos x - \sin x)\, dx is equal to :

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  4. Question 4

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

    14
    If ∫e−3log⁡x dx=f(x)+C\int e^{-3\log x}\, dx = f(x) + C, then f(x) is :

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  5. Question 5

    Inverse Trigonometric Functions. Asked once: 2024 (same type asked 3 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
    Assertion (A) : Domain of y=cos⁡−1(x)y = \cos^{-1}(x) is [−1,1][-1, 1]. Reason (R) : The range of the principal value branch of y=cos⁡−1(x)y = \cos^{-1}(x) is [0,π]−{π2}\left[0, \pi\right] - \left\{\dfrac{\pi}{2}\right\}.

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