JEE Mains · Maths · STD 11 - 6. permutation and combination
If \({ }^{2n } C _3:{ }^{n } C _3=10: 1\), then the ratio \(\left(n^2+3 n\right):\left(n^2-3 n+4\right)\) is
- A \(35: 16\)
- B \(65: 37\)
- C \(27: 11\)
- D \(2: 1\)
Answer & Solution
Correct Answer
(D) \(2: 1\)
Step-by-step Solution
Detailed explanation
\(\frac{{ }^{2 n} C_3}{{ }^{{ }^n} C _3}=10 \Rightarrow \frac{2 n (2 n -1)(2 n -2)}{ n ( n -1)( n -2)}=10\) \(n =8\) So \(\left(n^2+3 n\right):\left(n^2-3 n+4\right)=2\)
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