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  • If the coefficient of x in the expansion of <img alt="\left(x^2+\frac{k}{x}\right)^5" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28x%5E2&plus;%5Cfrac%7Bk%7D%7Bx%7D%5Cright%29%

If the coefficient of x in the expansion of \left(x^2+\frac{k}{x}\right)^5 is 270, then k = 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

T_{r+1}={ }^5 C_r\left(x^2\right)^{5-r}\left(\frac{k}{x}\right)^r

For coefficient of x, 10-2 r-r=1 \Rightarrow r=3

Hence T_{3+1}={ }^5 C_3\left(x^2\right)^{5-3}\left(\frac{k}{x}\right)^3

According to question, 10 k^3=270 \Rightarrow k=3

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Gunjita

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