Hello Priya Hivarekar, If somebody has studied 1 to 9 from Rajasthan and 10 to 12 from Tamil Nadu, then also she can get admission through State Quota, if she has domicile of Tamil Nadu or her parents must has domicile of Tamil Nadu.

The rules for domicile for Tamil Nadu are
Domicile candidates:

1.One must be a bonafide resident of the state

2.Students who have completed their Class 6 to 12 from the schools located in the state, they should not submit the nativity certificate. Such aspirants need to produce their parents birth certificate, ration card, SSLC/10/12 certificate or No Graduate Certificate in case parents are not literate.

3.Applicants from other states and living in Tamil Nadu will not be considered as domicile candidates and can get admission under open category.

4.Students who are not the domicile of the state but have studied Class 6 to 12 in schools of the state will be considered for admission under open category.

5.Domicile of Tamil Nadu who have studied Class 6 to 12 partly or completely in other states must furnish the true copies of parents certificates as mentioned above.

6.It must be noted that permanent resident certificate will not be accepted instead of nativity certificate

Hii Priya!

Since your daughter has completed her class 10th and 12th from Tamil Nadu, she must be having the bonafied certificate from the State. But, Tamil Nadu has no institutional quota, so, your daughter needs to attend the Rajasthan State counselling , subjective to fulfil the domicile criteria. You need a domicile in order to apply in Tamil Nadu.
Hope this helps.
Good luck!