Question
Evaluate :

$\int_0^1 \frac{\log x}{\sqrt{1-x^2}} \cdot d x$

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A manufacturer has three machine I, II, III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines.
The number of hours required for producing 1 unit each of M and N on the three machines are given in the following table:
Item
Number of hours required on machines
 
I
II
III
M
1
2
1
N
2
1
1.25
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