Short answer - Yes. 

Even foreign students can appear in the NTSE center in India at his/her own cost. Such candidates are not required to appear for Stage I exam. They can send application request through the head of their institution (along with an attested copy of Class 9th result) to Head Educational Survey Division, NCERT, New Delhi- 16. If such candidate clears the exam, he/she shall be granted scholarship for pursuing education in India only.

As per the official website:

Who can appear in this exam?

All students studying in class X in any type of recognized school including Kendriya Vidyalayas, Sainik Schools, Military Schools will be eligible to appear at the State Level Examination from the state in which the school is located.

Are there any eligibility conditions for appearing in the screening examination like qualifying percentage of marks... etc?

Eligibility criteria for Stage 1 varies from state to state. The State/UT may impose any eligibility condition for appearing in Stage 1 examination
 

Source: https://ivyti.es/1hff

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