The question tests knowledge of which medication acts as a bronchodilator specifically used in asthma. Salbutamol is a selective beta-2 adrenergic receptor agonist. When it binds to β2 receptors on bronchial smooth muscle, it activates adenylate cyclase, increases cAMP, and causes the smooth muscle to relax, producing rapid bronchodilation. This makes it the classic fast-acting rescue bronchodilator in asthma. The other options are not bronchodilators in the same immediate sense. Budesonide is an inhaled corticosteroid that reduces airway inflammation over time but does not quickly open the airways. Montelukast blocks leukotriene receptors to reduce inflammation and bronchoconstriction rather than providing immediate bronchodilation. Theophylline is a methylxanthine that can bronchodilate by inhibiting phosphodiesterase and increasing cAMP, but its use is limited by a narrow therapeutic window and interactions, so it’s less representative as a typical anti-asthmatic bronchodilator.

Ambroxol is a mucolytic used to thin and clear mucus, and in many markets it’s sold under the brand name Mucosolvan, a widely recognized trade name for this drug. The other names listed correspond to different medications—Norvasc is amlodipine (a blood pressure pill), Aspilets is aspirin, and Dulcolax is a laxative. So the brand name associated with Ambroxol is Mucosolvan.

The idea being tested is how anti-diarrheal drugs work by slowing intestinal movement to give water and electrolytes a chance to be absorbed, reducing stool frequency and liquidity. Loperamide fits this by acting as a μ-opioid receptor agonist in the enteric nervous system, which decreases gut smooth muscle tone and slows motility, letting more water be reabsorbed. It achieves this with minimal CNS effects because it stays largely in the gut and is expelled from the brain by P-glycoprotein, giving effective relief from diarrhea without significant central opioid effects. While other options can have anti-diarrheal actions (diphenoxylate is another opioid antidiarrheal, paregoric is an opium tincture, and bismuth subsalicylate has antisecretory and protective effects), loperamide is the classic peripherally acting agent most commonly recognized for this purpose.

The half-life in first-order elimination is determined by t1/2 = 0.693 × Vd / CL. This ties how far the drug distributes (Vd) to how quickly it’s cleared (CL). Plugging in Vd = 50 L and CL = 5 L/h gives Vd/CL = 50/5 = 10 h. Multiply by 0.693 to get t1/2 = 6.93 h. So the half-life is about 6.93 hours. The other numbers would require different Vd/CL ratios (for example, a much smaller ratio would yield a shorter t1/2, and a larger ratio would yield a longer t1/2).