PYQ Vault

Day 138: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. Asked once: 2024 (same type asked 4 times)

    34 (b)
    Evaluate : ∫−22x3+∣x∣+1x2+4∣x∣+4  dx\int_{-2}^{2} \frac{x^3 + |x| + 1}{x^2 + 4|x| + 4} \; dx

  2. Question 2

    Integrals. Asked once: 2025 (same type asked 4 times)

    31
    If ∫abx3 dx=0\displaystyle\int_a^{b} x^3\,dx = 0 and ∫abx2 dx=23\displaystyle\int_a^{b} x^2\,dx = \dfrac{2}{3}, then find the values of a and b.

  3. Question 3

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

    28 (b)
    Find : ∫x+3x2+4x+5 dx\int \dfrac{x + 3}{x^2 + 4x + 5}\, dx

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2025 (same type asked 4 times)

    21
    Find the domain of sin⁡−1(x2−3)\sin^{-1}(x^2 - 3).

  5. Question 5

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

    25 (b)
    Evaluate : tan⁡(sin⁡−11−cos⁡−1(−12))\tan \left( \sin^{-1} 1 - \cos^{-1} \left( -\frac{1}{2} \right) \right)