InterviewSolution
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InterviewSolution
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If the 4 th term in the expansion of `(a x + (1)/(x))^(n)` is (5)/(2)`, for all x `in` R then the values of a and n are respectivelyA. `(1)/(2),6`B. 1,3C. `(1)/(2),3`D. cannot be found |
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Answer» Correct Answer - a It is given that the fouth term in the expansion of `(ax+ (1)/(x))^(n) is (5)/(2)` `therefore ""^(n)C_(3) (a x)^(n-3) ((1)/(x))(3) = (5)/(2)` `rArr ""^(n)C_(3)a^(n-2) x^(n-6) = (5)/(2)` ….(i) `rArr n-6 = 0 [because ` RHS is independent of x] Putting n=6 in (i) , we get `""^(6)C_(3) a^(3) = (5)/(2) rArr a^(3) = (1)/(8) rArr a = (1)/(2)` Hence , n = 6 a ` = (1)/(2)` . |
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