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  • The coefficient of  in the expansion of <img alt="\left(1+x^2\right)^5(1+x)^4" src="https://entrancecorner.oncodeco

The coefficient of x^5 in the expansion of \left(1+x^2\right)^5(1+x)^4 is 

Option: 1

30


Option: 2

60


Option: 3

40


Option: 4

None of these


Answers (1)

best_answer

We have \left(1+x^2\right)^5(1+x)^4

=\left({ }^5 C_0+{ }^5 C_1 x^2+{ }^5 C_2 x^4+\ldots\right)\left({ }^4 C_0+{ }^4 C_1 x+{ }^4 C_2 x^2+{ }^4 C_3 x^3+{ }^4 C_4 x^4\right)So coefficient of x^5 in \left[\left(1+x^2\right)^5(1+x)^4\right]

={ }^5 C_2 \cdot{ }^4 C_1+{ }^4 C_3 \cdot{ }^5 C_1=60 .

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Riya

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