ExamBro
ExamBro
AP EAMCET · Maths · Binomial Theorem

If \(10{ }^n C_2=3^{n+1} C_3\), then the value of \(n\) is

  1. A \(3\)
  2. B \(10\)
  3. C \(7\)
  4. D \(9\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(9\)

Step-by-step Solution

Detailed explanation

\(10^n C_2=3^{n+1} C_3\) \(\frac{10 n !}{(n-2) ! 2 !}=\frac{3(n+1) !}{(n+1-3) ! \times 3 !}\) \(\begin{aligned} \Rightarrow & & \frac{10 n !}{2} & =\frac{3(n+1) n !}{3 \times 2} \\ \Rightarrow & & 10 & =n+1 \\ \Rightarrow & & n & =9\end{aligned}\)