AP EAMCET · Maths · Binomial Theorem
If \(10{ }^n C_2=3^{n+1} C_3\), then the value of \(n\) is
- A \(3\)
- B \(10\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
\(10^n C_2=3^{n+1} C_3\) \(\frac{10 n !}{(n-2) ! 2 !}=\frac{3(n+1) !}{(n+1-3) ! \times 3 !}\) \(\begin{aligned} \Rightarrow & & \frac{10 n !}{2} & =\frac{3(n+1) n !}{3 \times 2} \\ \Rightarrow & & 10 & =n+1 \\ \Rightarrow & & n & =9\end{aligned}\)
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