PYQ Vault

Day 8: CBSE Class 12 Maths

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

  1. Question 1

    Differential Equations. Asked 2 times: 2024, 2026

    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) : One of the particular solutions of the differential equation dydx=ex+y\dfrac{dy}{dx} = e^{x+y} can be ex+e−y=−2e^x + e^{-y} = -2. Reason (R) : ex+e−y=Ce^x + e^{-y} = C is the general solution of the differential equation dydx=ex+y\dfrac{dy}{dx} = e^{x+y}.

    Tap an option to check your answer.

  2. Question 2

    Integrals. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    27
    Evaluate : ∫0πsin⁡2026xsin⁡2026x+cos⁡2026x dx\int_{0}^{\pi} \dfrac{\sin^{2026} x}{\sin^{2026} x + \cos^{2026} x}\, dx

  3. Question 3

    Integrals. Asked 2 times: 2022*, 2026 (* = numbers or wording changed that year)

    27 (b)
    Evaluate : ∫−π6π2(sin⁡∣x∣+cos⁡∣x∣) dx\displaystyle\int_{\frac{-\pi}{6}}^{\frac{\pi}{2}} (\sin |x| + \cos |x|)\, dx

  4. Question 4

    Integrals. Asked 2 times: 2022, 2026

    26 (a)
    Find : ∫dxx1/2+x1/3\int \dfrac{dx}{x^{1/2} + x^{1/3}}

  5. Question 5

    Integrals. Asked 2 times: 2022, 2026

    28
    If ddx(F(x))=1ex+1\dfrac{d}{dx}(F(x)) = \dfrac{1}{e^x + 1}, then find F(x)F(x) given that F(0)=log⁡12F(0) = \log \dfrac{1}{2}.