I am an un-registered trader dealing in textile fabrics which was exempted from tax under the State VAT Act. If I get registered under the GST Act, will I be eligible to avail of input tax credit on my stock of goods lying on the appointed day?

Since the goods you are dealing with are exempted
from tax under the State Act, you will not be eligible to avail
input tax credit as SGST under the SGST Act, 2017 on your
stock of goods lying on the appointed day.
But, you will be eligible to enjoy CENVAT credit as Central
Tax on your stock if you have invoices or other prescribed
documents evidencing payment of excise duty under the
existing law and such invoices/prescribed documents
were issued not earlier than twelve months immediately
preceding the appointed day.