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The term independent of x in the expansion of ( (x + 1)(x2/3 + 1 - x1/3) - (x - 1)(x - x1/2) )10, x > 1, is :
(4) 210
x + 1 = (x1/3 + 1)(x2/3 - x1/3 + 1) x + 1x2/3 + 1 - x1/3 = x1/3 + 1
x - 1x - x1/2 = ( x - 1)( x + 1) x( x - 1) = 1 + x-1/2
Expression = (x1/3 - x-1/2 )10
Tr+1 = 10Cr (x1/3)10 - r(-x-1/2)r
Power of x: 10 - r3 - r2 = 0 20 - 5r = 0 r = 4
T5 = 10C4 (-1)4 = 210
Answer: (4)
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