InterviewSolution
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InterviewSolution
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Consider the expansion `(x^(2)+(1)/(x))^(15)`. What is the ratio of coefficient of `x^(15)` to term independent of x in the given expansion ?A. `1//64`B. `1//32`C. `1//16`D. `1//4` |
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Answer» Correct Answer - B Given expansion is `(x^(2)+(2)/(x))^(15)` `T_(r+1)=.^(15)C_(r)(x^(2))^(15-r)((2)/(x))^(r)` `=.^(15)C_(r)x^(30-2r)2^(r)x^(-r)=.^(15)C_(r)x^(30-3r).2^(r)` Now, Above term will be independent of x when `30 - 3r = 0 rArr r = 10` `therefore` Term independent of `x = .^(15)C_(10)2^(10)` Now, coeff of `x^(15)` When `30-3r = 15 rArr r = 5` `therefore` Required coeff `= .^(15)C_(5)2^(5)` Thus, Required Ratio = `(.^(15)C_(5).2^(5))/(.^(15)C_(10).2^(10))` `=((15!)/(5!(10!)))/((15!)/(10!5!)xx2^(5))=(1)/(2^(5))=(1)/(32)` |
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