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Please solve RD Sharma Class 12 Chapter 21 Differential Equations Exercise Case Study Based Question (CSBQ) Question 1 Subquestion (i) maths textbook solution.

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Answer: Option(a) \frac{d V}{d t}=-\lambda, \lambda>0 is a constant

Hint: Volume of sphere =\frac{4}{3} \pi r^{3} & then differentiate.

Given: Volume of a spherical balloon being deflated changes at a constant rate.

Solution: Volume of a balloon at a time, t= V.

Now as volume changes at constant rate, we can say

\begin{aligned} &\frac{d}{d t}(V) \alpha 1 \\ &\frac{d}{d t}(V)=\lambda \end{aligned}


Where \lambda is some constant.


 \frac{d V}{d t}=\lambda

But as the volume of balloon is deflated i. e., reduced so \lambda will be represented by -ve value.


\frac{d V}{d t}=-\lambda, \lambda>0 is a constant .

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