PYQ Vault

Day 67: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. Asked once: 2026 (same type asked 4 times)

    31
    Evaluate : ∫−π2π2cos⁡2x2x+1 dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \dfrac{\cos^2 x}{2^x + 1}\, dx

  2. Question 2

    Integrals. Asked once: 2026 (same type asked 4 times)

    11
    The value of ∫−5−11x dx\displaystyle\int_{-5}^{-1} \dfrac{1}{x}\,dx is equal to :

    Tap an option to check your answer.

  3. Question 3

    Integrals. Asked once: 2026 (same type asked 4 times)

    26
    Find : ∫x+29x−x2 dx\displaystyle\int \dfrac{x + 2}{\sqrt{9x - x^2}}\, dx

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2026 (same type asked 4 times)

    32
    Find the domain of p(x)=sin⁡−1(1−2x2)p(x) = \sin^{-1}(1 - 2x^2). Hence, find the value of xx for which p(x)=π6p(x) = \dfrac{\pi}{6}. Also, write the range of 2p(x)+π22p(x) + \dfrac{\pi}{2}.

  5. Question 5

    Inverse Trigonometric Functions. Asked once: 2026 (same type asked 4 times)

    23 (b)
    Evaluate : cos⁡[sin⁡−1(−1)−tan⁡−1(−3)]\cos[\sin^{-1}(-1) - \tan^{-1}(-\sqrt{3})].