InterviewSolution
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InterviewSolution
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In the expansion of `(1 + ax)^(n)`, the first three terms are respectively 1, 12x and `64x^(2)`. What is n equal to ?A. 6B. 9C. 10D. 12 |
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Answer» Correct Answer - B The first three terms in expansion of `(1+ax)^(n)` are `.^(n)C_(0), .^(n)C_(1)ax, .^(n)C_(2)a^(2)x^(2)` Given, `.^(n)C_(0)=1, .^(n)C_(1) ax = 12x, .^(n)C_(2)a^(2)x^(2)=64x^(2)` `rArr "nax" = 12x,(n(n-1))/(2)a^(2)=64` `rArr "na"=12 rArr a = (12)/(n)` `therefore (n(n-1))/(2)a^(2)=64 rArr (n(n-1))/(2)xx(144)/(n^(2))=64` `rArr(n-1)/(n)=(64xx2)/(144)=(8)/(9)` `therefore n = 9` |
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