Question

If the expansion of ${(x^3+\frac{1}{x^2})}^n$ contains a term independent of x, then the value n can be

• A. $18$
• B. $20$
• C. $24$
• D. $22$

Answer 1

Answer: (B)

$20$

Let (r+1) th term be independent of x

$T_{r+1}{=}^n{C}_r\left(x^3{)}^{n-r}\right(\frac{1}{x^2}{)}^r{=}^n{C}_r{x}^{3n-3r-2r}$

thus 3n must be a multiple of 5.

$3n=5k$

n=20 satisfies the value.