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As the patient is reportedly experiencing paralysis on the right side of her face, with loss of taste, dry mouth, and inability to close her right eye; it can be inferred that her Cranial Nerve VII (Facial), Cranial Nerve IX (Glossopharyngeal), Cranial Nerve X (Vagus), Cranial Nerve III (Oculomotor) have been affected.
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To be more specific:
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Paralysis of the right side of face = Cranial Nerve VII (Facial)
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Loss of taste = Cranial Nerve VII (Facial), Cranial Nerve X (Vagus), Cranial Nerve IX (Glossopharyngeal).
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Dry mouth = Cranial Nerve VII (Facial), Cranial Nerve IX (Glossopharyngeal)
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Inability to close right eye = Cranial Nerve VII (Facial), Cranial Nerve III (Oculomotor)
Reference:
Gibbons, J., & Sadiq, N. (2023, May 1). Neuroanatomy, Neural Taste Pathway - StatPearls. NCBI. https://www.ncbi.nlm.nih.gov/books/NBK545236/