PYQ Vault

Day 5: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked 2 times: 2025, 2026

    26
    A spherical balloon loses its volume due to escape of air from it in such a way that decrease of volume at any instant is proportional to its surface area. Show that the radius is decreasing at a constant rate.

  2. Question 2

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

    6
    A cylindrical tank is being filled with sand at a rate of 314 m3^3/h. If the radius of the tank is 10 m, then the height of sand in the tank increases at the rate of :

    Tap an option to check your answer.

  3. Question 3

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

    34
    Sketch the curve described by {(x, y):9x2+16y2=144}\{(x,\ y) : 9x^2 + 16y^2 = 144\} and find the area of the region enclosed by it, using integration.

  4. Question 4

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

    34
    Sketch the graph defined by {(x, y):x225+y225=1}\left\{(x,\ y) : \dfrac{x^2}{25} + \dfrac{y^2}{25} = 1\right\}. Find the area of the region of minor segment cut off by the line x=52x = \dfrac{5}{2}, using integration.

  5. Question 5

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

    33
    Using integration, find the area of the region bounded by y=5x+4y = 5x + 4, y=0y = 0, x=−1x = -1 and x=1x = 1.