Question

Given that the term of the expansion ${(x^{1/3}-x^{-1/2})}^{15}$ which does not contain $x$ is $5m$ where $mϵN$ then $m$ is equal to

• A. $1100$
• B. $1010$
• C. $1001$
• D. None of the above

Answer 1

The correct option is C $1001$

The general term for the above binomial expansion is

$T_{r+1}=(-1{)}^r{}^{15}{C}_r{x}^{\frac{30-5r}{6}}$
Now for the term independent of $x$,

$\frac{30-5r}{6}=0$

$30-5r=0$

$r=6$

Hence, Coefficient is ${}^{15}{C}_6$

$=5005$

$=5\left(1001\right)$

Hence

$m=1001$.