Question 6a
I'm assuming k is the variable representing any fo.
$ X_k[n]=Y_k[n] \, $
where
$ X_k[n]=\delta[n-k]\, $
and
$ Y_k[n]=(k+1)^2 \delta[n-(k+1)] \, $
Under this assumption the following system cannot possibly be time invariant because of the $ (k+1)^2 $ term.
