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Question

If the third term in the expansion of (1x+xlog10x)5 is 1,000, then x-equals

A
102
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B
103
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C
10
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D
None of these
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Solution

The correct option is A 102
T2+1
=T3
=5C2x3x2log10(x)
=103
Therefore
x3x2log10(x)=100
x2log10(x)3=100
Now x has to be in powers of 10.
Therefore
Let x=10k
Above equation reduces to
10k(2k3)=102
2k23k2=0
(2k+1)(k2)=0
k=2 and k=12
Hence x=102 and x=1012

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