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Question

The term independent of x in expansion of (x+1x2/3x1/3+1x1xx1/2)10 is :

A
4
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B
120
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C
210
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D
310
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Solution

The correct option is C 210
(x+1x2/3x1/3+1x1xx1/2)10
=((x1/3+1)(x2/3x1/3+1)(x2/3x1/3+1)(x1/2+1)(x1/21)x1/2(x1/21))10
=((x1/3+1)x1/21x1/2)10
=(x1/3+11x1/2)10
=(x1/3x1/2)10
The general term :
Tr= 10Cr(1)r(x1/3)r(x1/2)10r
= 10Cr(1)rxr/3x5+r/2
= 10Cr(1)rx5r65
5r65=0
r=6
T7= 10C6=10!4! 6!=210

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