Binomial Theorem
Coefficient of Specific Power in Binomial
nta_pyq_2023_apr
Grade 11
Question:
The coefficient of $x^5$ in the expansion of $\left(2x^3-\dfrac{1}{3x^2}\right)^5$ is
$\dfrac{80}{9}$
$9$
$8$
$\dfrac{26}{3}$
Step-by-Step Solution
Key Concept: $T_{r+1}=\binom{5}{r}(2x^3)^{5-r}\left(-\frac{1}{3x^2}\right)^r=\binom{5}{r}2^{5-r}\left(-\frac{1}{3}\right)^r x^{15-5r}$. Set $15-5r=5\Rightarrow r=2$.
$r=2$. Coefficient $=10\cdot8\cdot\frac{1}{9}=\frac{80}{9}$.
Correct Answer: 1