after grad I solely ran a coaching institution in my locality with help of my friends for 10 month.Can I add this as experience in cat form?

No you cannot add this coaching classes as your work experience because it was your personal work and the work experience which is accepted in the CAT exam is the one through registered companies.

Even the work experience in family business is also not approved until and unless your family business is properly RTO registered.

You can mention teaching as your hobby and strength but not as work experience. You can say that you have an ability to control and lead a group of people. Also you like to interact with people and share information, help each other. So due to these qualities only you were inspired to start a coaching.

Things I mentioned above is totally random to give you an example how you can make your this work as strength but yeah in short you won't be able to use it as a work experience.

All the best!!