InterviewSolution
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InterviewSolution
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Consider the expansion `(x^(2)+(1)/(x))^(15)`. Consider the following statements: 1. The term containing `x^(2)` does not exist in the given expansion. 2. The sum of the coefficients of all the terms in the given expansion is `2^(15)`. Which of the above statements is/are correct ?A. 2 onlyB. 3 onlyC. Both 1 and 3D. Neither 1 nor 3 |
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Answer» Correct Answer - C 1. For coefficient of `x^(2)`, `30 - 3r = 2 rArr r = (28)/(3), r notin N` So, `x^(2)` does not exist in the expansion Hence, Statement 1 is correct. 2. Now, `(x^(2)+(1)/(4))^(15)=.^(15)C_(0)(x^(2))^(15)+.^(15)C_(1)(x^(2))^(14)((1)/(x))+...+.^(15)C_(15)((1)/(x))^(15)` Put x = 1 both sides, we get `(1+1)^(15)=.^(15)C_(0)+.^(15)C_(1)+...+.^(15)C_(15)` `rArr 2^(15)=.^(15)C_(0)+.^(15)C_(1)+...+.^(15)C_(15)` Hence, Statement 2 is correct |
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