TS EAMCET · Maths · Binomial Theorem
If \(\left(1+2 x+3 x^2\right)^{10}\) \(=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}\) then \(\frac{a_2}{a_1}\) is equal to
- A 10.5
- B 21
- C 10
- D 5.5
Answer & Solution
Correct Answer
(A) 10.5
Step-by-step Solution
Detailed explanation
\(\left(1+2 x+3 x^2\right)^{10}\) \(=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}\) \(=\{1+x(2+3 x)\}^{10}\) Then by binomial expansion \(={ }^{10} C_0+{ }^{10} C_1 x(2+3 x)+{ }^{10} C_2 x^2(2+3 x)^2+\ldots\) Now, the coefficient of \(x\) in this expansion \(=2 \cdot{ }^{10} C_1\)…
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