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 10−15 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 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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