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Question

If the middle term in binomial expression of (1x+xsinx)10 is equal to 638, find the value of x.

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Solution

In the binomial expansion of (1x+xsinx)10,(102+1)th i.e., 6th term is the middle term.

It is given that :
T6=638

10C5(1x)105(xsinx)5=638

10!5!5!(sinx)5=638

(sinx)5=(12)5

sinx=12=sinπ6

x=nπ+(1)nπ6,nZ

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