IITPAL

In this article, you will get the answers to the questions " How to Choose Best Coaching Institute for your IITJEE Preparation?" Additionally,   I will also help you identify parameters to choose your dream coaching institute .   In this article, we will also discuss, whether coaching is required for JEE preparation?  Then should you join  online coaching/learning systems like BYJU etc or join classroom coaching ?  Let me begin with my first point of discussion i.e. why you should join a coaching institute for your jee preparation.  To perform your best in JEE, you need to have a deeper understanding of Physics Chemistry, and Mathematics. These conceptual subjects require experiential learning. Guided learning from experienced mentors is very important here. Our schooling system fails in the application of the conceptual learning part.  NCERT tells you what of the concepts but fails to teach you why and how of concepts.  A JEE expert teachers have...

  A man wishes to fence in a perfectly square field which is to contain just as many acres as there are rails in the required fence. Each hurdle, or portion of the fence, is seven rails high, and two lengths would extend one pole (16½ ft.): that is to say, there are fourteen rails to the pole, lineal measure. Now, what must be the size of the field?

Ramanujam (The man Who Knew Infinity) The great Indian Mathemagician Shrinivasan Ramanujam never had any close friends and someone asked him the reason. He replied, “ I always wanted to have a good friend, but unfortunately I am not getting anyone matching my expectations” . The man asked what your expectation? Ramanujam replied,  “The numbers 284 and 220 are exemplary friends and I wish is to have that kind of friendship with someone” The man got confused and asked, “How do this friendship and these two numbers connect?” Ramanujam clarified and asked the man to find all the proper Divisors of these two numbers. After a little difficulty, the person listed the divisors:- Proper Divisors of 284 including 1 are 1, 2, 4, 71, 142. and proper Divisors of 220 including 1 are: 1, 2, 4 ,5, 10, 11, 20, 22, 44, 55, 110. Ramanujam asked him to calculate the total of these divisors for each number. The friend did that and the answer was surprising, he got :- 1 +2+ 4+ 71+ 142 = 220 and 1+ 2 +4+...

  Combinatorics is not difficult, it's different.  We deal it very similar to other branches of mathematics, i.e.  use the equation/formulae  to get an answer. And this fails. in some sense, every problem in combinatorics requires a different formula. My conclusion is " you can not master combinatorics by remembering a few set of formulae."  Combinatorics can be treated as SCIENTIFIC COUNTING.  To b egin with, combinatorics the most basic part is the fundamental theorem of counting, create your own logic of connecting information given in the problem, and practice a lot more problem. Every good combinatorics problem requires a new road map, create it. The biggest confusion for beginners is in fact when to apply  Permutation and when to apply Combination.  Here is an easy way that can clear you concept: With permutations, every little detail matters. Ali, Bobby and Charl is different from Charl, Bobby, and Ali. Combinations, on the other hand, are ...

  Every once in a while, I hear puzzles about 100 prisoners and a meticulous, demanding warden. All of these puzzles share a common characteristic, a set of prisoners must work together to devise a clever scheme to thwart the warden. I hear these puzzles often enough that each time they reappear, I view them with an increased level of understanding corresponding to the stage of my mathematics education. Any problem may have a solution, but, sometimes, that solution may not be the most efficient one possible. For example, suppose you want to find something in your room but don’t remember where you put it. You can either search the room by yourself. Or you can call your (many) friends to help you. From a correctness standpoint, both solutions are correct. You’ll find what you’re looking for eventually. But from an algorithmic standpoint, the second solution where you search in parallel with your friends is better because it has a shorter runtime. The same holds for solutions to the 1...

We all know the easy way to solve the quadratic equation,           a x²+bx+c =0. W e use the quadratic formula for roots. We also have access to similar formulae for roots of cubic equations and quartic equations. The formula for roots of a cubic equation  ax 3 +bx 2 +cx+d=0 is  A similar complex looking formulae exist for roots of a quartic equation. But myster i ously we do not have any such formula for roots of 5 or higher degree polynomials. It seems as if, we can not construct the solutions of a degree 5 or higher degree polynomials just by using addition, subtraction, multiplication, division, and radicals in its coefficients.  Why so? what is so special in this 5-degree polynomial? These were questions that haunted the young Frenchman  Evariste Galois  in the 18th century. He developed a new mathematical object called a “group” that solved this issue in a surprisingly cool way. Galois being shot in a duel.  Image from...

What is π ? It's the ratio of the circumference of a circle to its diameter. Or it's the area of a circle of radius 1 or something like that. Everyone knows that.  Wrong. Well, it's not exactly wrong. It is true that π has these properties. But that's not its essence, it's not what it fundamentally π is. The stuff with the circles is just one aspect of π and not the most profound one. π somehow depends on the geometry of our universe or the way we measure angles, or lengths, or areas. There are tons, believe me). That's false, of course. π π doesn't care at all about the structure of the universe or real-life circles. Euler's formula e^i π +1=0 What then, is π ? And why is it so ubiquitous? The answer lies with a profound, incredible, and beautiful (complex) exponential function. #pie