In this case the wife can apply for government job even after marriage in an upper caste. The caste of a person does not change after marriage be it girl or boy. The girl belongs to SC caste and so marrying in upper caste does not affect her employment. She is free to apply for job under SC caste and her new surname.
Under Article 335A of Constitution of India the claims of Scheduled caste and Scheduled tribes in terms of employment to services and post in government job shall be taken into consideration. The wife can use any of the surname either her birth surname or her after marriage surname.
However, Article 335 also states that the acknowledgement of such claims shall be consistent with the concerns of efficiency. Though the provision permitting the state to provide reservation in employment finds mention in the Fundamental Rights chapter of the Constitution and Article 335 is in the chapter on Special Provisions Relating to Certain Classes so marriage does not affect the caste of any person.
If wife’s Id proofs have the surname of husband that does not affect the employment criteria. The wife will be eligible for any govt. job irrespective of her marriage in upper caste.
Reference: Article 335A of Constitution of India
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