PYQ Vault

Day 113: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2026 (same type asked 3 times)

    26
    The volume of a wooden block in the shape of a cube increases at a constant rate as the air becomes moist during the rainy season. Show that the rate of change of its surface area varies inversely as the length of edge of the cube.

  2. Question 2

    Application of Derivatives. Asked once: 2024 (same type asked 3 times)

    5
    If the sides of a square are decreasing at the rate of 1⋅51{\cdot}5 cm/s, the rate of decrease of its perimeter is :

    Tap an option to check your answer.

  3. Question 3

    Application of Derivatives. Asked once: 2024 (same type asked 3 times)

    23
    Sand is pouring from a pipe at the rate of 15 cm3^3/minute. The falling sand forms a cone on the ground such that the height of the cone is always one-third of the radius of the base. How fast is the height of the sand cone increasing at the instant when the height is 4 cm ?

  4. Question 4

    Application of Integrals. Asked once: 2025 (same type asked 3 times)

    31
    Sketch the graph of y=∣x+3∣y = |x + 3| and find the area of the region enclosed by the curve, xx-axis, between x=−6x = -6 and x=0x = 0, using integration.

  5. Question 5

    Application of Integrals. Asked once: 2025 (same type asked 3 times)

    24
    Calculate the area of the region bounded by the curve x29+y24=1\frac{x^2}{9} + \frac{y^2}{4} = 1 and the x-axis using integration.