Final answer:
The symptoms likely to be observed in a patient with a non-functional thyroid gland are lethargy and mental sluggishness, indicating hypothyroidism.
Step-by-step explanation:
Among the listed options, the symptoms likely to be observed in a patient with a completely non-functional thyroid gland would be lethargy and mental sluggishness. This is indicative of hypothyroidism, a condition in which the thyroid gland is underactive. The other symptoms such as increased heart rate, exophthalmos, and high metabolic rate are associated with hyperthyroidism, which occurs when the thyroid gland is overactive. Hypothyroidism usually results in a decreased metabolic rate, with symptoms including weight gain, cold sensitivity, and reduced mental activity as the thyroid hormone is essential for regulating metabolism and energy use in the body.