yeah you should take a cbse school for class 12thand simultaneously you can prepare for iitjee there are two types of coaching in india for that online and offline
i personlly reccoment you online classes as i its a best balance between boards and jee you dont need to travel anywhere to take classes
you dont need for the next class if u have any doubt that can be solved anytime online only
for further enquiry drop you email id our team will contact you