WBJEE · Maths · Binomial Theorem
If the co-efficients of \(x^2\) and \(x^3\) in the expansion of \((3+a x)^9\) be same, then the value of ' \(a\) ' is
- A \(\frac{3}{7}\)
- B \(\frac{7}{3}\)
- C \(\frac{7}{9}\)
- D \(\frac{9}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{7}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints : }(3+a x)^9={ }^9 \mathrm{C}_0 3^9+{ }^9 \mathrm{C}_1 3^8(a x)+{ }^9 \mathrm{C}_2 37(a x)^2+{ }^9 \mathrm{C}_3 3{ }^6(a x)^3 \\ & { }^9 \mathrm{C}_2 3^7 a^2={ }^9 \mathrm{C}_3 3{ }^6 \mathrm{a}^3 \\ & \frac{9}{7}=a \end{aligned} \]
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