PYQ Vault

Day 25: CBSE Class 12 Maths

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

  1. Question 1

    Differential Equations. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    11
    The general solution of the differential equation dydx=yx\dfrac{dy}{dx} = \dfrac{\sqrt{y}}{\sqrt{x}} is

    Tap an option to check your answer.

  2. Question 2

    Differential Equations. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    29 (b)
    Find the particular solution of the differential equation xydydx=(x+2) (y+2)xy \frac{dy}{dx} = (x + 2) \, (y + 2), given that y(1)=−1y(1) = -1.

  3. Question 3

    Integrals. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    28
    If I1=∫−π/4π/4dx1+cos⁡2xI_1 = \int_{-\pi/4}^{\pi/4} \frac{dx}{1 + \cos 2x} and I2=∫−1/21/2∣x∣ dxI_2 = \int_{-1/2}^{1/2} \left| x \right| \, dx, then show that I1−4I2=0I_1 - 4I_2 = 0.

  4. Question 4

    Integrals. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    27 (a)
    Evaluate : ∫π125π12dx1+cot⁡x\displaystyle\int_{\frac{\pi}{12}}^{\frac{5\pi}{12}} \dfrac{dx}{1 + \sqrt{\cot x}}

  5. Question 5

    Integrals. This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026

    30
    Evaluate : ∫01xsin⁡−1x dx\int_{0}^{1} x \sin^{-1} x \, dx