Input tax eligibility under gst

I am registered dealer in say Tamilnadu .I do a service to client in delhi .For that purposes i stay in hotel . Hotel charges me CGST +SGST (since for him both is intra)

Now my question
1. whether i am eligible for CGST against my other CGST payments.
2. I may not be eligible for SGST since i dont have any registration in Delhi , am i right...

Whether any thing changes i supply goods instead of service

Thanks in advance