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In the expansion of `(x+x^(2)+x^(3)+…….) (1+x+x^(2)+x^(3)) (x^(2)+x^(3)+x^(4)+……+x^(10))` the coefficient of `x^(6)` isA. `10`B. `18`C. `30`D. `12` |
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Answer» Correct Answer - A In the expansion ……….. `(x+x^(2)+…….)………` Coefficient of `x^(6)` in the expansion `(x+x^(2)+…..)` `(1+x+x^(2)+x^(3))(x^(2)+…….+x^(10))` = Coefficient of `x^(6)` in the expension `x^(3)(1+x+x^(2)+……) (1+x+x^(2)+x^(3))(1+x+x^(2)+....+x^(8))` = Coefficient of `x^(3)` in the expansion `(1-x^(4))(1-x^(9))(1-x)^(-3)` = Coefficient of `x^(3)` in the expansion `(1-x)^(-3) = ^(5)C_(3) = 10` |
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