InterviewSolution
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InterviewSolution
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The power of x which has the greatest coefficient inthe expansion of `(1+x/2)^10`A. 2B. 3C. 4D. 5 |
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Answer» 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. |
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