AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^5\) in the expansion of \(\left(1+x^2\right)^5(1+x)^4\), is :
- A 60
- B 50
- C 40
- D 56
Answer & Solution
Correct Answer
(A) 60
Step-by-step Solution
Detailed explanation
We have, \(\left(1+x^2\right)^5(1+x)^4\) \(=\left[1+{ }^5 C_1 x^2+{ }^5 C_2 x^4+\ldots+\left(x^2\right)^5\right]\) \(\left[1+{ }^4 C_1 x+{ }^4 c_2 x^2+{ }^4 C_3 x^3+x^4\right]\) Coefficient of \(x^5={ }^5 C_1 \cdot{ }^4 C_3+{ }^5 C_2 \cdot{ }^4 C_1\)…
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