The term independent of x in expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)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 C210 (x+1x2/3−x1/3+1−x−1x−x1/2)10 =((x1/3+1)(x2/3−x1/3+1)(x2/3−x1/3+1)−(x1/2+1)(x1/2−1)x1/2(x1/2−1))10 =((x1/3+1)−x1/2−1x1/2)10 =(x1/3+1−1−x−1/2)10 =(x1/3−x−1/2)10 The general term : Tr=10Cr(−1)r(x1/3)r(x−1/2)10−r =10Cr(−1)rxr/3x−5+r/2 =10Cr(−1)rx5r6−5 ∴5r6−5=0 ⇒r=6 T7=10C6=10!4!6!=210