Binomial Theorem
Coefficient of Given Power in Binomial Expansion
nta_pyq_2023_apr
Grade 11
Question:
The coefficient of $x^{18}$ in the expansion of $\left(x^4-\dfrac{1}{x^3}\right)^{15}$ is ____________.
Step-by-Step Solution
Key Concept: General term: $T_{r+1}=\binom{15}{r}(x^4)^{15-r}\left(-\frac{1}{x^3}\right)^r=\binom{15}{r}(-1)^r x^{60-7r}$. Set $60-7r=18\Rightarrow r=6$.
$r=6$. Coefficient $=\binom{15}{6}=5005$.
Correct Answer: 5005