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 : 47
Total: 50
Value of h (in m) for which ‌
dC
dh
=0
is
Explanation: Since,
C=‌
12500
h
+400h2

∴‌‌‌
dC
dh
=‌
−12500
h2
+800h

‌ Put ‌‌‌‌
dC
dh
=0

‌∴‌‌
−12500
h2
+800h‌
=0

‌⇒‌800h3‌=12500
‌⇒h3‌=‌
125
8

‌⇒‌h‌=‌
5
2
=2.5m
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