IIT Preparation

Devoting one full year for JEE examination preparation has its own merits and demerits. Dropping a year means that you will get sufficient amount of time to prepare for competitive exams. You can work on your weakness and further sharpen your strengths. It will allow you take mock up test and help to score good ranking in competitive exams. However, one year is a long time so the possibility of you may change your goals and objectives. You may become lethargic because of availability of time and lesser pressure. You may waste time. If you are confident of keeping the momentum, dedication, determination, readiness to work on a plan, will to achieve your objective and support of family; you may consider dropping a year for competitive exams. It is worth try option. If you are not confident of cracking JEE after one year of preparation then you choose any other college to do engineering. If you are unable to do B.Tech from IIT, you can do M.Tech from IIT after scoring well in GATE or do MBA after cracking CAT examination to gain competitive advantage in career.

The answer is 1/3 sq units. Actually, in the given question, we have 2 equations i.e., y=mod x and y greater than or equal to x square. The graphs of both the equations are drawn and next solve the equations.
We get the common meeting points as (0,0) and (1,1). So integrate, the equation (mod x-x square) from 0 to1 and multiply it with 2 because the area we got is only the area that was covered in the 1st quadrant.
By multiplying, we get the area that is covered in the 2nd quadrant too. My suggestion is that when you get the equation with greater than or equal to or less than or equal to, solve the equation consider only one condition that is equal to and solve the equation.
All the best.