Input tax claim

Services by an entity registered under Section 12AA of Income-tax Act, 1961 by way of charitable activities are exempt from whole of the GST, therefore no ITC can be claimed.

the hospitals don't have GSTIN  hence there is no question about being able to claim ITC or not.

on the other hand if it a medical store or any other type of assessee that is providing auxiliary services to hospitals that are registered with GST may claim ITC, if the purchase is in the nature of their real input.

what will you do after taking ITC when your output supply is exempt .

Where there is no GST output on account of exempt supply, there is no option of GST refund. Refund arises in cases where there is zero rated supply, i.e. supplies to SEZ, Exports or in special cases such as inverted duty structure (ITC on inputs only). 

Where any machinery is used to provide exempt and taxable supplies - ITC can be claimed as per section 17 r/w Rule 43 (computation to be as per the Rules). 

Generally medical products fall under 5%, 12% and 18%, therefore appropriate classification of procurements could reduce cost.