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 1015 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 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 250m3 and he charged 400X (depth) )2. Association will like to have minimum cost.

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Question : 49
Total: 50
Value of x (in m ) for minimum cost is
Explanation: For minimum cost, put
dC
dh
=0
, we get
h=2.5m
At h=2.5,
d2C
dh2
>0


(Hence, minimum)
Value of x at minimum cost
x=
250
h

=
250
2.5
=10m
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