Here is a list of IITs and other institutes that offer admission through the IIT JAM Mathematics score along with their respective cutoffs:

1. Indian Institute of Technology (IIT), Bombay:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Bombay varies from year to year. However, it generally ranges between 40-50 marks (out of 100).

2. Indian Institute of Technology (IIT), Delhi:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Delhi also varies annually. It usually falls between 35-45 marks.

3. Indian Institute of Technology (IIT), Kanpur:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Kanpur ranges from 30-40 marks.

4. Indian Institute of Technology (IIT), Kharagpur:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Kharagpur is generally around 30-40 marks.

5. Indian Institute of Technology (IIT), Madras:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Madras varies but is usually in the range of 30-40 marks.

6. Indian Institute of Technology (IIT), Guwahati:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IIT Guwahati is generally around 25-35 marks.

7. Indian Statistical Institute (ISI), Kolkata:

- Cutoff: The cutoff for the IIT JAM Mathematics score at ISI Kolkata is usually around 30-40 marks.

8. National Institute of Technology (NIT), Warangal:

- Cutoff: The cutoff for the IIT JAM Mathematics score at NIT Warangal ranges from 20-30 marks.

9. Harish-Chandra Research Institute (HRI), Allahabad:

- Cutoff: The cutoff for the IIT JAM Mathematics score at HRI Allahabad is generally around 20-30 marks.

10. Institute of Mathematical Sciences (IMSc), Chennai:

- Cutoff: The cutoff for the IIT JAM Mathematics score at IMSc Chennai is usually in the range of 20-30 marks.

Please note that these cutoffs are approximate values and can vary from year to year depending on various factors such as the difficulty level of the exam and the number of applicants.

It is always advisable to check the official websites of the respective institutes for the most accurate and up-to-date information regarding admissions and cutoffs.