InterviewSolution
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InterviewSolution
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The expansion of `(x-y)^(2), n ge 5` is done in the descending power of x. If the sum of the fifth and sixth terms is zero, then `(x)/(y)` is equal toA. `(n-5)/(6)`B. `(n-4)/(5)`C. `(5)/(n-4)`D. `(6)/(n-5)` |
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Answer» Correct Answer - B `(X-Y)^(n), n ge 5` General term, `T_(r+1)=n_(c_(r))x^(n-r)(-y)^(r)`. `T_(5) + T_(6) = 0` `rArr [n_(c_(4))x^(n-4)(-y)^(4)]+[n_(c_(5))x^(n-5)(-y)^(5)]=0` `rArr n_(c_(4))x^(n-4)y^(4)-n_(c_(5))x^(n-5)y^(5)=0` `rArr n_(c_(4))x^(n-4)y^(4)=n_(c_(5))x^(n-5)y^(5)` `rArr (x^(n-4-n+5))/(y)=(n_(c_(5)))/(n_(c_(4)))rArr (x)/(y)=(cancel(n!))/(5!(n-5)!)xx(4!(n-4)!)/(cancel(n!))` `=(cancel(4!)(n-4)cancel((n-5)!))/(5 xx cancel(4!) cancel((n-5)!))=(n-4)/(5)` |
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