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Question

Term independent of x in the expansion of (x1x2)3n (where n is even natural number)

A
3n!n!×2n!
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B
3n!n!
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C
3n!2n!
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D
3n!(n!)2
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Solution

The correct option is A 3n!n!×2n!
Tr+1=(1)r 3nCrx3nr×(1x2)r
Tr+1=(1)r 3nCrx3n3r
For independent term
Put 3n3r=0r=n.

So, Tn+1 is free from x.
And, Tn+1=(1)n 3nCn=3nCn

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