Binomial Theorem
Coefficient in multi-term expansion
MJMT_Full_Test_08
Grade 12
Question:
The coefficient of $x^{1012}$ in the expansion of $(1+x^n+x^{253})^{10}$ where $n\leq22$ is any positive integer, is
${}^{253}C_4$
$4n$
${}^{10}C_4$
$1$
Step-by-Step Solution
Key Concept: Since $253=23\times11$ and $1012=253\times4$, and $n\leq22$: no multiples of $n$ can combine with $253$ to reach $1012$ except from the $(1+x^{253})^{10}$ term alone.
${}^{10}C_4$.
Correct Answer: 3