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CBSE Class 12 Math 2022 Term I Solved Paper

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Case Study
In a residential society comprising of 100 houses, there were 60 children between the ages of 101510-15 years. They were inspired by their teachers to start composting to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house, children convinced the Residents welfare association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of 50\text{₹} 50 per square metre for space so that there is no misuse of the space and Resident welfare association takes it seriously. Association hired a labourer for digging out 250m3250 \text{m}^3 and he charged 400X\text{₹} 400 \text{X} (depth) )2)^2. Association will like to have minimum cost.
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Question : 47 of 50
Marks: +1, -0
Value of hh (in m) for which dCdh=0\frac{dC}{dh}=0 is
Explanation: Since,
C=12500h+400h2C = \frac{12500}{h} + 400 h^2
dCdh=12500h2+800h\therefore \frac{dC}{dh} = \frac{-12500}{h^2} + 800 h
PutdCdh=0\text{Put} \frac{dC}{dh}=0
12500h2+800h=0\therefore \frac{-12500}{h^2} + 800 h = 0
800h3=12500\Rightarrow 800 h^3 = 12500
h3=1258\Rightarrow h^3 = \frac{125}{8}
h=52=2.5 m\Rightarrow h = \frac{5}{2} = 2.5 \text{ m}
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