JEE Mains · Maths · STD 11 - 6. permutation and combination
If \(\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11\), then \(n\) satisfies the equation
- A \(n^2 + n - 110 =0\)
- B \(n^2 + 2n - 80 =0\)
- C \(n^2 +3n- 108=0\)
- D \(n^2 + 5n - 84 =0\)
Answer & Solution
Correct Answer
(C) \(n^2 +3n- 108=0\)
Step-by-step Solution
Detailed explanation
\(\frac{{^{n + 2}{C_6}}}{{^{n - 2}{P_2}}} = 11\) \( \Rightarrow \frac{{\frac{{(n + 2)(n + 1)n(n - 1)(n - 2)(n - 3)}}{{6.5.4.3.2.1}}}}{{\frac{{(n - 2)(n - 3)}}{{2.1}}}} = 11\) \( \Rightarrow (n + 2)(n + 1)n(n - 1) = 11.10.9.4\) \( \Rightarrow n = 9\)…
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