Correct Answer - b
Let the coefficient of `(r +1)^(th)` term be the greatest
coefficient in the expansion of `(1 + (x)/(2))^(10)`. Then,
`((T_(r+1))/(T_(r)))_(x=1) gt 1 and ((T_(r+2))/(T_(r+1)))_(x=1)lt1`
`rArr (""^(10)C_(r)((1)/(2))^(r))/(""^(10)C_(r-1)((1)/(2))^(r-1)) gt 1 and (""^(10)C_(r+1)((1)/(2))^(r+1))/(""^(10)C_(r)((1)/(2))^(r))lt1`
`rArr (11 -r)/(2r) gt 1 and (10 -r)/(2(r +1)) lt 1`
`rArr 8 lt 3r lt 11`
`rArr r = 3`
Now,
`T_(r+1) = ""^(10)C_(r) ((1)/(2))^(r) rArr T_(4) = ""^(10)C_(3) ((1)/(2))^(3) x^(3)`
Hence, the power of x having the greatest coefficient in 3.
