Dear Yshikag,
You could have given complete information. Where your institute is located? For what type of competitive exam do you provide coaching? When did you start your institute?
Since yours is a service industry, it will take time to establish brand. Word of Mount (WOM) plays key role in promoting your business. Nevertheless, you may concentrate your marketing activities within radius of 10 KM from your institute.
I can given one idea that could be beyond 10 KM radius. In every city, there are some places where forms for the competitive exams are sold. These are generally road-side squatters. These squatters also sell magazines for the competitive exams. I recommend you approaching them and finding out possibility of promoting your institute by means of providing free envelops. You may insert fliers in the competitive magazines sold out through these squatters.
Secondly, it would be tempting to induct all types of students, nevertheless, you can be selective and select only the worthy types. This will help you in marketing your finished products i.e. the students who have taken coaching from your institute and pass the competitive exam.
Thirdly, explore possibly of co-branding with the institute that provide coaching for Class X and XII. This is your prospective market. It need not be outward branding it it can be in-class branding.
Lastly, find out where tuition classes for engineering students or any other students are conducted. You can do branding there also.
P.S.: - You are from institute that provide coaching for competitive exams. In competitive exams, test on English is always included. Nevertheless, your post or quality of English does not reflect your profession. You could have done little better on that count! While your post is not egregious per se, it is not excellent either.
All the best!
Dinesh Divekar