No, you are not eligible to appear for the NEET exam if you do not have English as a core subject in Class 12. As per the NEET eligibility criteria set by NTA and NMC, candidates must have passed:
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Physics,
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Chemistry,
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Biology/Biotechnology, and
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English as core subjects in 10+2.
English is compulsory, and you must pass it along with the other three main subjects. Even if you score well in PCB, not having English as a core subject will disqualify you from the NEET exam.