PYQ Vault

Day 23: CBSE Class 12 Maths

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

  1. Question 1

    Application of Integrals. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    35
    Find the area of the smaller region bounded by the curves x225+y216=1\frac{x^2}{25} + \frac{y^2}{16} = 1 and x5+y4=1\frac{x}{5} + \frac{y}{4} = 1, using integration.

  2. Question 2

    Application of Integrals. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    33
    Find the area of the region {(x,y):x2+y2≤1≤x+y}\{(x, y) : x^2 + y^2 \le 1 \le x + y\}, using integration.

  3. Question 3

    Integrals. Asked 2 times: 2022, 2023

    32
    Evaluate : ∫0πx1+sin⁡x dx\displaystyle\int_{0}^{\pi} \dfrac{x}{1 + \sin x}\,dx

  4. Question 4

    Integrals. Asked 2 times: 2022, 2023

    28 (a)
    Evaluate : ∫02π11+esin⁡x dx\displaystyle\int_{0}^{2\pi} \dfrac{1}{1 + e^{\sin x}}\,dx

  5. Question 5

    Integrals. Asked 2 times: 2022, 2023

    27
    Evaluate : ∫134−xx+4−x dx\int_{1}^{3} \frac{\sqrt{4-x}}{\sqrt{x} + \sqrt{4-x}} \, dx