InterviewSolution
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InterviewSolution
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Find the constant term in the expansion of `(sqrtx+1/(3x^2))^10`.A. 5B. 8C. 45D. 90 |
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Answer» Correct Answer - A Let `r^(th)` term is independent of x. `T_(r) = .^(n)C_(r)x^(r)y^(n-r)` `=.^(10)C_(r)(sqrt(x))^(r)((1)/(3x^(2)))^(10-r)` `=.^(10)C_(r)((1)/(3))^(10-r).(sqrt(x))^(r)((1)/(x^(2)))^(10-r)` Equating the coefficient of x to zero. `rArr x^(r//2).x^(-2(10-r)=x^(0)` `rArr (r)/(2)-20 + 2r = 0` `rArr (5)/(2)r = 20 rArr r = 8` Coefficient `=.^(10)C_(r)((1)/(3))^(10-r)` `=.^(10)C_(8)((1)/(3))^(10-8)=(10xx9)/(2)xx(1)/(9)=5` |
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