The term independent of x in the expansion of x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 1 0 is

The term independent of xin the expansion of x+1x2/3-x1/3+1-x-1x-x1/210  is
  1. 210
  2. 310
  3. 4
  4. 120

Solution

We know, x2/3-x1/3+1x1/3+1=x+1

⇒x+1x2/3-x1/3+1=x1/3+1

Also, x-1x-x=x-1x+1xx-1=x+1x=1+x-1/2

Hence, the given binomial becomes x1/3-x-1/210.

General term =10Cr-1rx10-r3x-r2

Hence, for term independent of x.

 We get 10-r3=r2

20-2r=3r

r=4
∴ Term Independent of x=10C4=210
 

Asked in: JEE Main 2013 (07 Apr)

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