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General Term of Binomial Expansion

Coefficient o...

Question

Coefficient of $x^{11}$ in the expansion of $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is

A

1051

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B

1106

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C

1113

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D

1120

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Solution

The correct option is C $1113$
$2 a + 3 b + 4 c = 11$
Possible combination of $(a, b, c)$
$(0, 1, 2), (1, 3, 0), (2, 1, 1), (4, 1, 0)$

Hence, the coefficient of $x^{11}$ in $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is :

$(^{4} C_{0} \times^{7} C_{1} \times^{12} C_{2}) + (^{4} C_{1} \times^{7} C_{3} \times^{12} C_{0}) + (^{4} C_{2} \times^{7} C_{1} \times^{12} C_{1}) + (^{4} C_{4} \times^{7} C_{1} \times^{12} C_{0}) = 462 + 140 + 504 + 7 = 1113$

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General Term of Binomial Expansion

Standard XIII Mathematics

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