Can i claim deduction u/s 80d and 80ddb both?

Yes you can avail benefit of both of  80D and 80DDB deduction. But for the purpose of 80DDB you have to keep  proof of prescripttion made my doctor. and only the amount which is not received by insurance company is eligible to deduction Under section 80DDB. Means out of total expenditure on your mother, the amount which is received from insurance company will be deducted and balance will be eligile for deduction u/s 80DDB. 

Yes you van claim deduction under both the section- 80D AND 80DDB. Deduction u/s 80DDB can be claimed irrespective of whether the person is covered under any health insurance policy or not. However, remember that the amount of deduction claimed will be reduced by the amount received from an insurer or reimbursed by the employer for medical treatment of the said person.
 

Both can be claimed

Section 80D: Health Insurance Premium Deduction

For Self/Spouse/Dependent Children: Up to ₹25,000 (₹50,000 if Senior Citizen) for health insurance premium. Additional ₹5,000 for preventive health check-ups, included in the above limit.

For Parents: Up to ₹25,000 (₹50,000 if Senior Citizen) for their health insurance premium. Additional ₹5,000 for preventive health check-ups, included in the above limit.

Section 80DDB: Medical Treatment Deduction

For Self/Dependent: Up to ₹40,000 (₹1,00,000 if Senior Citizen) for specified disease-related medical treatment.