Binomial Theorem
Binomial Coefficient Ratio — Solving for n
nta_pyq_2023_apr
Grade 11
Question:
If ${}^{2n}C_3:{}^nC_3=10:1$, then the ratio $(n^2+3n):(n^2-3n+4)$ is
Step-by-Step Solution
Key Concept: $\dfrac{(2n)(2n-1)(2n-2)}{n(n-1)(n-2)}=10\Rightarrow\dfrac{4(2n-1)}{n-2}=10\Rightarrow n=8$.
$n=8$. Ratio $=\frac{88}{44}=2:1$.
Correct Answer: 4