InterviewSolution
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InterviewSolution
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What is the middle term in the expansion of `((xsqrt(y))/(3)-(3)/(ysqrt(x)))^(12)` ?A. `C(12,7)x^(3)y^(-3)`B. `C(12,6)x^(-3)y^(3)`C. `C(12,7)x^(-3)y^(3)`D. `C(12,6)x^(3)y^(-3)` |
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Answer» Correct Answer - D In the expansion of `((xsqrt(y))/(3)-(3)/(ysqrt(x)))^(12)`, then middle term is `(12)/(2)+1=7^(th)" term ". (r+1)_(th)" term, "` `T_(r+1)=""^(12)C_(r)[(xsqrt(y))/(3)]^(12-r)cdot(-(3)/(ysqrt(x)))^(r)` `therefore" "T_(7)=T_(6+1)=""^(12)C_(6)((xsqrt(y))/(3))^(6)(-(3)/(ysqrt(x)))^(6)` `=""^(12)C_(6)(x^(6)y^(3))/(y^(6)x^(2))=""^(12)C_(6)x^(3)y^(-3)=C(12,6)x^(3)y^(-3)` |
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