If C3 2n:C3 n=10:1, then the ratio n2+3n:n2-3n+4 is

2nC3C3 n=10:1 ⇒(2n)(2n-1)(2n-2)n(n-1)(n-2)=1012(2n-1)×2n-2=101⇒4n-2=5n-10⇒n=8n2+3nn2-3n+4=64+2464-24+4=8844=21

If C3 2n:C3 n=10:1, then the ratio n2+3n:n2-3n+4 is

2nC3C3 n=10:1 ⇒(2n)(2n-1)(2n-2)n(n-1)(n-2)=1012(2n-1)×2n-2=101⇒4n-2=5n-10⇒n=8n2+3nn2-3n+4=64+2464-24+4=8844=21

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If ${}^{2 n}C_{3} : {}^{n}C_{3} = 10 : 1$ , then the ratio $(n^{2} + 3 n) : (n^{2} - 3 n + 4)$ is

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65 : 37

27 : 11

35 : 16

2 : 1

answer is D.

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$\frac{^{2 n} C_{3}}{{}^{n}C_{3}} = 10 : 1 \Rightarrow \frac{(2 n) (2 n - 1) (2 n - 2)}{n (n - 1) (n - 2)} = \frac{10}{1}$

$\frac{2 (2 n - 1) \times 2}{n - 2} = \frac{10}{1} \Rightarrow 4 n - 2 = 5 n - 10 \Rightarrow n = 8$

$\frac{n^{2} + 3 n}{n^{2} - 3 n + 4} = \frac{64 + 24}{64 - 24 + 4} = \frac{88}{44} = \frac{2}{1}$

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If C3 2n:C3 n=10:1, then the ratio n2+3n:n2-3n+4 is

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If ${}^{2 n}C_{3} : {}^{n}C_{3} = 10 : 1$ , then the ratio $(n^{2} + 3 n) : (n^{2} - 3 n + 4)$ is