To solve this problem, we need to identify which functions are NOT under the control of thyroid hormones. Let's analyze each option:$\newline \bullet$A. Maintenance of water and electrolyte balance:$\newline$ - Thyroid hormones do not directly regulate water and electrolyte balance. This is primarily controlled by hormones like aldosterone and antidiuretic hormone (ADH).$\newline \bullet$B. Regulation of basal metabolic rate:$\newline$ - Thyroid hormones are crucial for regulating the basal metabolic rate (BMR). They increase the metabolic activity of most tissues.$\newline \bullet$C. Normal rhythm of sleep-wake cycle:$\newline$ - The sleep-wake cycle is primarily regulated by the circadian rhythm and hormones like melatonin, not thyroid hormones.$\newline \bullet$D. Development of immune system:$\newline$ - The development of the immune system is not directly controlled by thyroid hormones. It involves various other factors and hormones.$\newline \bullet$E. Support the process of RBC formation:$\newline$ - Thyroid hormones do support erythropoiesis (RBC formation) by stimulating erythropoietin production.$\newline$Based on the analysis, the functions NOT under the control of thyroid hormones are:$\newline \bullet$C. Normal rhythm of sleep-wake cycle$\newline \bullet$D. Development of immune system$\newline$Therefore, the correct answer is Option 3: C and D only.