How to Ace Sequences and Series


Sequences and series mainly cover arithmetic progression, geometric progression and harmonic progression. These, along with some other special series can be very frustrating to many IIT aspirants, as they require cumbersome calculations and predictions which may go wrong most of the times. However, the formulae are easy to remember, but difficult to apply. The arithmetic progression or AP contains the maximum type of questions, therefore varieties are also present in it. The questions asked are not usually formulae based and require the ability to predict the series by understanding. They usually consume much time and a lot of practice is required to proceed in the correct direction. The experience required comes from gradually increasing the level of practice problems and even then a lot of intuition is required to complete it. Sometimes, algorithms can be developed for approaching a certain type of problem, but they fail too easily if the series has changed even a little.

In the olden pattern, the JEE used to contain many long questions about the series, but since the change in pattern, it has been converted into small questions which can be completed in a reasonable time. Therefore, it is advisable to master the easy questions involving small tricks and not waste too much time trying to crack hard questions which have no chance of coming in the JEE. This topic is usually taught well in the coaching institutions and relevant questions can also be obtained from the study material provided. Selective study is the best way to approach it and remember that most of the other aspirants also find this topic tough, so don’t be discouraged if you are not able to solve a problem.
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Keep your eyes upon the goal

 On July 4, 1952, Florence Chadwick was on her way to becoming the first woman to swim the Catalina Channel. She had already conquered the English Channel. The world was watching. Chadwick fought the dense fog, bone-chilling cold and many times, the sharks. She was striving to reach the shore but every time she looked through her goggles, all she could see was the dense fog. Unable to see the shore, she gave up.
Chadwick was disappointed when she found out that she was only half a mile from the coast. She quit, not because she was a quitter but because her goal was not in sight anywhere. The elements didn't stop her. She said,
"I'm not making excuses. If only I had seen the land, I could have made it. " 

Two months later, she went back and swam the Catalina Channel. This time, in spite of the bad weather, she had her goal in mind and not only accomplished it but beat the men's record by two hours.

”Obstacles are those frightful things you see when you take your eyes off your goal. “--Henry Ford
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How to Ace Quadratic Equations in IIT


Quadratic equation forms the basic part of algebra in JEE mathematics. A bit onthis topic is already learnt by many students in their previous classes. A quadratic equation is relatively easy to understand. Like Trigonometry, direct questions from quadratic equation are rarely asked in JEE Advance. Question from quadratic equation will always be clubbed with any other part of the JEE math syllabus. But for JEE Main, which is relatively simple there will be direct questions from the topic. Graphical representation of the given quadratic equation is very useful. Always try to solve questions by graphical methods as they consume less time and efforts. Within a limited time, you can solve the question quickly. As you know that equation of the parabola is quadratic, and its proficiency in quadratic equation will definitely help you for topic co-ordinate geometry. Here are some points that you must keep in your mind while solving questions of quadratic equation to avoid getting wrong answers:


  1. Pay attention to signs of roots (positive and negative) to avoid getting negative marks after solving complete questions.
  2. After getting the solution of an equation, fill in back the solution in equation to check whether it’s actually a solution or not. There are some cases when the solution you get doesn’t satisfy the equation and you end up getting negative marks. 
  3. Many conditions and standard result which is there in quadratic equation are quite confusing and therefore try to remember conditions using their graphical representation so that it will be retained in your memory for a long time. Quadratic equation plays important role in physics questions as well as in some part of chemistry, so don’t neglect it. Also Quadratic equation is well related to complex numbers, as the origin of complex numbers is because of no real solution condition of quadratic equations.
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How to Measure Success


True success is measured by the feeling of knowing you have done a job well and have achieved your objective. Success is not measured by our position in life but by the obstacles we overcame to get there. Success in life is not determined by how we are doing compared with others, but by how we are doing compared with what we are capable of doing. Successful people compete against themselves. They better their own record and keep improving constantly. Success is not measured by how high we go up in life but by how many times we bounce back when we fall down. It is this bounce back ability that determines
success.

" I feel true success comes from being able to work and the love for it. " - Kiana Tom
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