The pair of compounds, which cannot exist together in a solution is NaHCO3 and NaOH.

Explanation:
When considering the solubility of compounds in a solution, it is important to understand the concept of solubility rules and the interactions between different ions in a solution.

Solubility of NaHCO3:
NaHCO3, also known as sodium bicarbonate or baking soda, is a soluble compound. It readily dissolves in water to form sodium ions (Na+) and bicarbonate ions (HCO3-). The dissolution of NaHCO3 in water can be represented by the following equation:

NaHCO3(s) → Na+(aq) + HCO3-(aq)

Since NaHCO3 is soluble, it can exist in a solution with water.

Solubility of NaOH:
NaOH, also known as sodium hydroxide or caustic soda, is another soluble compound. It dissolves in water to form sodium ions (Na+) and hydroxide ions (OH-). The dissolution of NaOH in water can be represented by the following equation:

NaOH(s) → Na+(aq) + OH-(aq)

Since NaOH is soluble, it can also exist in a solution with water.

Explanation of the correct answer:
The correct answer is option A, NaHCO3 and NaOH. These two compounds cannot exist together in a solution because they react with each other to form a new compound and water. The reaction between NaHCO3 and NaOH is a neutralization reaction that produces sodium carbonate (Na2CO3), water (H2O), and carbon dioxide (CO2). The balanced equation for this reaction is:

2NaHCO3 + NaOH → Na2CO3 + 2H2O + CO2

This reaction occurs because the hydroxide ions (OH-) from NaOH react with the bicarbonate ions (HCO3-) from NaHCO3 to form water and carbonate ions (CO3-2). The sodium ions (Na+) remain unchanged in the reaction.

Therefore, NaHCO3 and NaOH cannot exist together in a solution because they react with each other to form new compounds and water.