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Given that, $f(x)=x^{2}$ and $g(x)=2^{x};\forall x\in \mathbb{R}$

Now, we can find the functions value which is required.

- $f(1)=1^{2}= 1 $
- $g(1)=2^{1}= 2 $
- $f(2)=2^{2}= 4 $
- $f(6)=6^{2}= 36 $

The value of $f(f(g(x))+g(f(x)))$ at $x=1 : $

Now, $f(f(g(1))+g(f(1)))= f(f(2)+g(1)) =f(4+2)=f(6) =36$

$\therefore$ The value of $f(f(g(x))+g(f(x)))$ at $x=1$ is $36.$

Correct Answer $:\text{C}$