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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 : 48 of 50
Marks: +1, -0
  d2Cdh2\;\frac{d^2 C}{d h^2} is given by
Explanation: Since,
    dCdh=12500h2+800h\therefore \;\; \frac{d C}{d h} = \frac{-12500}{h^2}+800 h
    d2Cdh2=(2)×12500h3+800\therefore \;\; \frac{d^2 C}{d h^2} = \frac{-(-2) \times 12500}{h^3}+800
  d2Cdh2=25000h3+800\Rightarrow \; \frac{d^2 C}{d h^2} = \frac{25000}{h^3}+800
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