Explanation:

Litmus paper:
Litmus paper is a paper strip that is used to test the acidity or alkalinity of a substance. It is made by treating paper with a natural dye extracted from lichens. Litmus paper comes in two colors: red and blue. Red litmus paper turns blue in the presence of a base or alkaline substance, while blue litmus paper turns red in the presence of an acid.

Red litmus turning blue:
When a substance turns red litmus paper blue, it indicates that the substance is a base or alkaline in nature. Bases are substances that release hydroxide ions (OH-) when dissolved in water. These hydroxide ions react with the red litmus dye, causing it to turn blue.

Options:
a) Vinegar: Vinegar is a weak acid, which means it releases hydrogen ions (H+) when dissolved in water. It does not contain hydroxide ions, so it will not turn red litmus paper blue. Therefore, option 'a' is incorrect.

b) Baking soda solution:
Baking soda (sodium bicarbonate) is a base. When it is dissolved in water, it releases hydroxide ions (OH-). These hydroxide ions react with the red litmus dye, turning it blue. Therefore, option 'b' is correct.

c) Lemon juice: Lemon juice is acidic in nature and contains citric acid. It releases hydrogen ions (H+) when dissolved in water. It does not contain hydroxide ions, so it will not turn red litmus paper blue. Therefore, option 'c' is incorrect.

d) Soft drinks: Soft drinks are generally acidic due to the presence of carbonic acid and other acids. They release hydrogen ions (H+), but not hydroxide ions (OH-). Therefore, soft drinks will not turn red litmus paper blue. Therefore, option 'd' is incorrect.

Conclusion:
From the given options, only baking soda solution (option 'b') will turn red litmus paper blue as it is a base and releases hydroxide ions when dissolved in water.