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Question

The term independent of x in the expansion of (x+1x2/3x1/3+1x1xx1/2)10, where x0,1 is equal to

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Solution

(x+1x2/3x1/3+1x1xx1/2)10=(x+1x2/3x1/3+1×1+x1/31+x1/3x1xx1/2×x+x1/2x+x1/2)10=((x1/3+1)x+1x)10=(x1/3x1/2)10

Tr+1= 10Crx10r3(x)r2
10r3=r2r=4
put r=4, T5= 10C4=210

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