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← JEE Main 2017 · 9 Apr · Shift 1
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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 67

The coefficient of x−5x^{-5} in the binomial expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)10\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}\right)^{10}, where x≠0,1x\ne0,1, is :

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Answer and worked solution

Official answer: A

x+1x2/3−x1/3+1=x1/3+1\dfrac{x+1}{x^{2/3}-x^{1/3}+1}=x^{1/3}+1 (sum of cubes) and x−1x−x=1+x−1/2\dfrac{x-1}{x-\sqrt x}=1+x^{-1/2}. The expression is (x1/3−x−1/2)10(x^{1/3}-x^{-1/2})^{10}, whose general term has power 10−r3−r2\frac{10-r}3-\frac r2. That equals −5 at r=10r=10, with coefficient (−1)10=1(-1)^{10}=1.

Topics:General and middle terms
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