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If the coefficient of  x^7 \text { in }\left(a x^2+\frac{1}{b x}\right)^{11}is equal to the coefficient of x^{-7} \text { in }\left(a x-\frac{1}{b x^2}\right)^{11}then ab =

Option: 1

1


Option: 2

1/2


Option: 3

2


Option: 4

3


Answers (1)

best_answer

For coefficient of  x^7 \text { in }\left(a x^2+\frac{1}{b x}\right)^{11} ; n=11, \alpha=2, \beta=1, m=7

r=\frac{11.2-7}{2+1}=\frac{15}{3}=5

Coefficient of  x^7 \text { in } T_6={ }^{11} C_5 a^6 \cdot \frac{1}{b^5}x^7 \text { in } T_6={ }^{11} C_5 a^6 \cdot \frac{1}{b^5}......(1) and for coefficient of x^{-7} \text { in }\left(a x-\frac{1}{b x^2}\right)^{11} ; n=11, \alpha=1, \beta=2, m=-7 ; \quad r=\frac{11.1+7}{3}=6

 Coefficient of  x^{-7} \text { in } T_7={ }^{11} C_6 \cdot a^5 \cdot \frac{1}{b^6}.....(2)

From equation (1) and (2), we get

ab=1

 

Posted by

Devendra Khairwa

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