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Question

The term independent of x in expansion of
(x+1x2/3x1/3+1x1xx1/2)10is
  1. 210
  2. 310
  3. 4
  4. 120


Solution

The correct option is A 210
Given expression can be written as
((x1/3+1)(x+1x))10=(x1/3+111x)10=(x1/3x1/2)10
general term =Tr+1=10Cr(x1/3)10r(x1/2)r=10Crx10r3(1)rxr2=10Cr(1)r.x10r3r2
Term will be independent of x when 10r3r2=0
r=4
So, required term =T5=10C4=210

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