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Application of Derivatives

JEE Main 2025 (Online) 23rd January Evening ShiftMCQMedium📈 Topic in 3% papers+4−1
Ques. 1JEE Main 2025, 23 January (Evening Shift)

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm, the ice-cream melts at the rate of 81 cm3/min and the thickness of the ice-cream layer decreases at the rate of 14 cm/min. The surface area (in cm2) of the chocolate ball (without the ice-cream layer) is :

  1. 128
  2. 196
  3. 225
  4. 256

Answer

(4) 256

Solution

Only the ice-cream shrinks: V= 43 (R3-r3) with r fixed.

[figure]

dVdt=4 R2 dRdt 81=4 R2 14 R=9

r=R-1=8 cm

Surface area = 4 r2=256 cm2

Answer: (4)

Keep practising — Application of Derivatives

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Let f(x)= 0x2 t2-8t+15et dt, x . Then the numbers of local maximum and local minimum points of f, respectively, are :

  1. 3 and 2
  2. 2 and 2
  3. 2 and 3
  4. 1 and 3

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