InterviewSolution
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InterviewSolution
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Find the 6th term of the expansion `(y^(1//2) + x^(1//3))^(n)` , if the binomial coefficient of 3rd term from the end is 45. |
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Answer» Correct Answer - `252y^(5//2)x^(5//3)` Coefficient of 3rd term from the beginning is always equal to the coefficient of 3rd term frm the end. Now, `T_(r+1) - .^(n) C(y^(1//2))^(n-r)*(x^(1//3))r.` Coefficient of `T_(3) = .^(n)C_(2) = (n(n-1))/2.` ` (n(n-1))/2 = 45 rArr n^(2) - n-90 = 0 rArr n^(2) - 10n + 9n - 90 = 0` `rArr ( n-10 (n+9) = 0 rArr n = 10` `:. T_(6) = T_(5+1) = .^(10)C_(5) (y^(1//2))^((10-5))*(x^(1//3))^(5)` `= (10 xx 9 xx 8 xx 7 xx 6)/(5 xx 4 xx 3 xx 2 xx 1) xxy^(5//2)x^(5//3) = 252y^(5//2)x^(5//3).` |
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