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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 : 50 of 50
Marks: +1, -0
Total minimum cost of digging the pit (in ₹) is
Explanation: Total minimum cost,
(At 2.5)
  C=  12500h+400h2\; C=\; \frac{12500}{h}+400 h^2
C=  125002.5+400(2.5)2\Rightarrow C=\; \frac{12500}{2.5}+400(2.5)^2
C=5000+2500\Rightarrow C=5000+2500
C=7500\Rightarrow C=\text{₹} 7500
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