If $a$ is positive real number and if the middle term of ${\left(\frac{a}{3}+3\right)}^8$is $1120$ then value of $a$ is 

Middle term of ${\left(\frac{a}{3}+3\right)}^8$is the $\left(\frac{8}{2}+1\right)\mathrm{th}$ or

$5^{\text{th }}$ term. We have 

$T_5=T_{4+1}{=}^8{C}_4{\left(\frac{a}{3}\right)}^4(3{)}^4=70a^4$

We are given  $T_5=1120\Rightarrow 70a^4=1120$

$\Rightarrow a^4=16=2^4\Rightarrow a=\pm 2$