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JEE Main20252 Apr 2025Morning ShiftMathematicsBinomial TheoremActual

The term independent of x in the expansion of ( (x+1) (x^ 2 / 3 +1-x^ 1 / 3 ) - (x+1) (x-x^ 1 / 2 ) )¹⁰, x 1 is:

Options

  1. A210
  2. B150
  3. C240
  4. D120

Correct answer

A. 210

Step-by-step solution

aligned & ( (x+1) (x^ 2 3 +1-x^ 1 3 ) - (x-1) (x-x^ 1 2 ) )¹⁰ & = ( (x^ 1 3 +1 )- ( x +1 x ) )¹⁰ & = (x^ 1 3 - 1 x )¹⁰ & T_ r+1 = ¹⁰ C_r(x)^ 10-r 3 (-1)^r(x)^ - r 2 & 10-r 3 - r 2 =0 & (20-2 r)-3 r=0 & r¹⁰=4 & ¹⁰ C₄(-1)^4=210 aligned

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