PYQ Vault

Day 9: CBSE Class 12 Maths

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

  1. Question 1

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

    28 (a)
    Find : ∫cos⁡x(2+sin⁡x) (4+sin⁡x) dx\int \dfrac{\cos x}{(2 + \sin x)\,(4 + \sin x)}\, dx

  2. Question 2

    Integrals. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    27 (a)
    Find : ∫x−sin⁡x1−cos⁡x dx\displaystyle\int \dfrac{x - \sin x}{1 - \cos x}\,dx

  3. Question 3

    Integrals. Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)

    9
    ∫dx25−16x2\displaystyle\int \dfrac{dx}{\sqrt{25 - 16x^2}} is equal to :

    Tap an option to check your answer.

  4. Question 4

    Integrals. Asked 2 times: 2025, 2026

    10
    If ∫01dxex+e−x=tan⁡−1e+k\displaystyle\int_0^1 \dfrac{dx}{e^x + e^{-x}} = \tan^{-1} e + k, then the value of k is :

    Tap an option to check your answer.

  5. Question 5

    Inverse Trigonometric Functions. Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)

    21
    Evaluate : tan⁡−1(−13)+cot⁡−1(13)+tan⁡−1(sin⁡(−π2))+tan⁡−1(tan⁡2π3)\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) + \cot^{-1}\left(\dfrac{1}{\sqrt{3}}\right) + \tan^{-1}\left(\sin\left(-\dfrac{\pi}{2}\right)\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right)