The correct answer is: between.
The word “between” is used to indicate a relationship between two or more things. In this case, India, Pakistan, and China are three countries that have border problems with each other. The problems exist between the countries, not among them or in them or on them.
The word “among” is used to indicate a relationship between three or more things that are considered to be a group. In this case, India, Pakistan, and China are not considered to be a group, so the word “among” would not be appropriate.
The word “in” is used to indicate a relationship between something and a place. In this case, the border problems do not exist in a place, so the word “in” would not be appropriate.
The word “on” is used to indicate a relationship between something and a surface. In this case, the border problems do not exist on a surface, so the word “on” would not be appropriate.