Binomial Theorem
Binomial Coefficients
nta_pyq_2025_apr
Grade 11
Question:
Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of $(1 + x)^{2n-1}$. If $2A = 5B$, then $n$ is equal to:
Step-by-Step Solution
Key Concept: $A = {}^{2n-1}C_{29}$ and $B = {}^{2n-1}C_{11}$. Set up the condition $2A = 5B$ and simplify using factorial form.
$A = {}^{2n-1}C_{29}$, $B = {}^{2n-1}C_{11}$. The condition $2 \cdot {}^{2n-1}C_{29} = 5 \cdot {}^{2n-1}C_{11}$ simplifies to $2n - 12 = 30$, giving $n = 21$.
Correct Answer: 21