PYQ Vault

Day 38: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    9
    The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is :

    Tap an option to check your answer.

  2. Question 2

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    26
    A thin metallic wire in the shape of a circular ring has its enclosed area increasing at a uniform rate when heated. Show that the rate of change of circumference varies inversely as the radius.

  3. Question 3

    Application of Derivatives. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    22
    A room freshner bottle in the shape of an inverted cone sprays the perfume at regular intervals such that volume of the perfume in the bottle decreases at the steady rate of 1 mm3^3/min. Find the rate at which level of perfume is dropping at an instant when level of perfume in the bottle is 10 mm, if the semi-vertical angle of conical bottle is π6\frac{\pi}{6}.

  4. Question 4

    Application of Integrals. This type asked 3 times: 2022, 2025, 2026. This one: 2026

    33
    Using integration, find the area of the region enclosed by the curve y=∣x−6∣y = |x - 6|, the x-axis, and between x=4x = 4 and x=8x = 8.

  5. Question 5 (case study, 4 parts)

    Application of Integrals. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by C1C_1 ; x2+y2=64x^2 + y^2 = 64. There is a circular pond with a fountain in the middle of the roundabout whose equation is given by C2:x2+y2=4C_2 : x^2 + y^2 = 4. Based on the given information, answer the following questions :
    38 (i)
    Represent the given equations C1C_1 and C2C_2 with the help of a diagram.
    38 (ii)
    Express y as a function of xx, (y=f(x))(y = f(x)), for both C1C_1 an C2C_2.
    38 (iii) (a)
    Using integration find the area of region covered by the roundabout.
    38 (iii) (b)
    Using integration, find the area of region covered by circular pond.