Test Index

CBSE Class 12 Math 2022 Term I Solved Paper

Show Para  Hide Para 
Case Study
In a residential society comprising of 100 houses, there were 60 children between the ages of 10−1510-15 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.
© examsnet.com
Question : 49 of 50
Marks: +1, -0
Value of xx (in m\mathrm{m} ) for minimum cost is
Explanation: For minimum cost, put   dCdh=0\; \frac{d C}{dh}=0, we get
h=2.5mh=2.5 \mathrm{m}
   At       h=2.5,  d2Cdh2>0\; \text{ At }\; \;\; h=2.5, \; \frac{d^2 C}{d h^2}>0
$ $
(Hence, minimum)
Value of xx at minimum cost
x  =250hx\;=\sqrt{\frac{250}{h}}
  =2502.5=10m\;=\sqrt{\frac{250}{2.5}}=10 \mathrm{m}
© examsnet.com
Go to Question: