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He is in fact, I am certain, one of the greatest mathematicians according to any criteria, let it be because he had no formal education, or because of the 3000 odd identities and theorems he came up with.anyway i don’t want to compare but i am just trying to say the striking things i saw in his life.Anyway I would first show the marklist Ramanujan acquired in the 1st year examinations.Roughly speaking, for these things,Ramanujan’s name is seen everywhere around the world, even if some might disagree.•Magic Square•Brocard – Ramanujan Diophatine equation•Dougall – Ramanujan identity•Hardy – Ramanujan number•Landau – Ramanujan constant•Ramanujan’s congruences•Ramanujan – Nagell equation•Ramanujan – Peterssen conjecture•Ramanujan – Skolem’s theorem•Ramanujan – Soldner constant•Ramanujan summation•Ramanujan theta function•Ramanujan graph•Ramanujan’s tau function•Ramanujan’s ternary quadratic form•Ramanujan’s prime•Ramanujan’s costant•Ramanujan’s sum•Rogers – Ramanujan’s identityNow, let us see a quote of an English Mathematician“Srinivasa Ramanujan was a mathematician so great that his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last thousand years.”He continued thus: “His leaps of intuition confound mathematicians even today, a century after his death. His papers are still plumbed for their secrets. His theorems are being applied in areas- polymer chemistry, computers, astrophysics, molecular physics, even (it has been recently suggested) cancer – scarcely imaginable during his lifetime. And always the nagging question: What might have been, had he been discovered a few years earlier, or lived a few years longer?”Now just see Ramanujan’s childhood prodigy:Teacher: n/n = 1. Any number divided by itself is one. If there are 3 apples and there are three students, each one will get one apple. Likewise if there are 1000 children and 1000 pens, each will get one pen.Ramanujan: What about 0/0? If there are 0 apples and 0 students, will each still get one?Teacher got perplexed!Ramanujan’s Explanation: 0/0 can be anything, the zero in the numerator could be many times 0 in the denominator, and vice versa.Just before the age of 10, in November 1897, he passed his primary examinations in English, Tamil, geography and arithmeticWith his scores, he stood first in the district. That year, Ramanujan entered Town Higher Secondary School where he encountered formal mathematics for the first time.By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his house.He was later lent a book on advanced trigonometry written by S. L. LoneyHe completely mastered this book by the age of 13 and discovered sophisticated theorems on his own.Now Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method. Its like this:It is easy to solve simple equation of the first degree, e.g., 3a = 15. And we are taught how to solve second degree equations with the power of x as 2.Ramanujan found his own method in solving not only cubic equations but also equations of fourth degree.Next year not knowing that quintic equations, or equations with power of x as 5, cannot be solved, he tried and failed in his attempt.In 1903 when he was16, Ramanujan came across the book by G. S. Carr on A Synopsis of Elementary Results in Pure and Applied Mathematics, a collection of 4865 formula and theorems without proofThe book is generally acknowledged as a key element in awakening the genius of RamanujanThe next year, he had independently developed and investigated the Bernoulli numbers and had calculated Euler's constant up to 15 decimal placesWhen he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics as an outstanding student who deserved scores higher than the maximum possible marksHe received a scholarship to study at Government Arts College, Kumbakonam, However, Ramanujan could not focus on any other subjects and failed most of them, losing his scholarship in the processHe later enrolled at Pachaiyappa' College in Madras. He again excelled in mathematics but performed poorly in other subjectsRamanujan failed his Fine Arts degree exam in December 1906 and again a year laterWithout a degree, he left college and continued to pursue independent research in mathematics. At this point of his life, he lived in extreme poverty and was suffering from starvation.Deplorable Condition of Ramanujan is expressed in his own words:“When food is the problem, how can I find money for paper? I may require four reams of paper every month.”On 14 July 1909, Ramanujan was married to a nine-year old girl, Janaki Ammal (21 March 1899 - 13 April 1994)After the marriage, Ramanujan developed a hydrocele problemsHis family did not have the money for the operation, but in January 1910, a doctor volunteered to do the surgery for freeAfter his successful surgery, Ramanujan searched for a jobHe stayed at friends' houses while hewent door to door around the city of Chennai looking for a clerical positionTo make some money, he tutored some students at Presidency College who were preparing for their examRamanujan met deputy collector V. Ramaswamy Aiyer, who had recently founded the Indian Mathematical SocietyRamanujan, wishing for a job at the revenue department where Ramaswamy Aiyer worked, showed him his mathematics notebooksAs Ramaswamy Aiyer later recalled:“I had no mind to smother his genius by an appointment in the lowest level as clerk in the revenue department.”Ramaswamy Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends.Some of these friends looked at his work and gave him letters of introduction to R. Ramachandra Rao, the district collector of Nellore and the secretary of the Indian Mathematical SocietyRamachandra Rao was impressed by Ramanujan's research but doubted that it was actually his own work !Ramanujan's friend, C. V. Rajagopalachari, persisted with Ramachandra Rao and tried to clear any doubts over Ramanujan's academic integrityRao listened as Ramanujan discussed elliptic integrals, hypergeometric series, and his theory of divergent series, through which Rao was convinced of Ramanujan's mathematical brilliance . When Rao asked him what he wanted, Ramanujan replied that he needed some work and financial supportRamanujan continued his mathematical research with Rao's financial aid taking care of his daily needsWith the help of Ramaswamy Aiyer, Ramanujan had his work published in the Journal of Indian Mathematical SocietyOne of the first problems he posed in the journal was to evaluate:He waited for a solution to be offered in three issues, over six months, but failed to receive any. At the end, Ramanujan supplied the solution to the problem himselfHe formulated an equation that could be used to solve the infinitely nested radicals problem. Using this equation, the answer to the question posed in the Journal was simply 3In early 1912 he got a job in the Madras Accountant Generals office with a salary of Rs 20 per month.Later he applied for a position under the Chief Accountant of the Madras Port TrustHe was Accepted as a Class III, Grade IV accounting clerk making 30 rupees per monthHe used to Spend spare time doing Mathematical ResearchIn the spring of 1913, Narayana Iyer and Ramachandra Rao tried to present Ramanujan's work to British mathematiciansOne mathematician, M. J. M. Hill of University College London, commented that although Ramanujan had "a taste for mathematics, and some ability", he lacked the educational background and foundation needed to be accepted by mathematiciansOn 16 January 1913, Ramanujan wrote to G. H. HardyComing from an unknown mathematician, the nine pages of mathematics made Hardy initially view Ramanujan's manuscripts as a possible "fraud“ !Hardy recognized some of Ramanujan's formulae but others "seemed scarcely possible to believe"G.H. Hardy was an academician at Cambridge UniversityHe was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.Later on Ramanujan wrote to G.H.HardyHardy recognised some of his formulae but other “seemed scarcely possible to believe”. Some of them were –Initially, G. H. Hardy thought that the works of Ramanujan were fraud because most of them were impossible to believe.But eventually ,he was convinced and interested in his talent.This is one approximation formula of Pi mentioned in Ramanujan’s letters:Hardy was also impressed by some of Ramanujan's other work relating to infinite series:This second one was new to Hardy, and was derived from a class of functions called hypergeometric series which had first been researched by L. Euler and Carl F. Gauss.After he saw Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy commented that the "[theorems] defeated me completely; I had never seen anything like them before”He figured that Ramanujan's theorems "must be true”Hardy asked a colleague, J. E. Littlewood, to take a look at the papersLittlewood was amazed by the mathematical genius of RamanujanRamanujan’s notebook referring calculus and number theory:Ramanujan boarded the S.S.Nevasa on 17 March 1914 and arrived in London on 14th AprilRamanujan began working with Hardy and LittlewoodHardy received 120 theorems from him in 1st 2 letters but there were many more results in his notebookRamanujan spent nearly 5 years in CambridgeRamanujan was awarded the B.A degree by Research in March 1916 at an age of 28 years for his work on Highly Composite Numbers.He was elected a Fellow of the Royal Society of London in February 1918 at an age of 30 years.He was the second Indian to become FRS.( First one was in 1841).He was elected to a Trinity College Fellowship as the FIRST INDIAN.During his five years stay in Cambridge he published twenty one research papers containing theorems.A few words regarding the 1729, Ramanujan NumberHardy arrived in a cab numbered 1729He commented that the number was uninteresting or dull.Instantly Ramanujan claimed that it was the smallest natural number which can be written as sum of cubes in 2 ways1729 = sum of cubes of 12 and 1/ sum of cubes of 10 and 9.Actually only this much is available in the popular version of the story.But Ramanujan had worked extensively on this number and made some simple reuslts along with other startling contributions.1729 = 7 x 13 x 19 product of primes in A.P1729 divisible by its sum of digits.1729 = 19 x 911729 is a sandwich number or HARSHAD number."Ramanujan was using 1729 and elliptic curves to develop formulas for a K3 surface," Ono says. "Mathematicians today still struggle to manipulate and calculate with K3 surfaces. So it comes as a major surprise that Ramanujan had this intuition all along."Ono had worked with K3 surfaces before and he also realized that Ramanujan had found a K3 surface, long before they were officially identified and named by mathematician André Weil during the 1950s.Just as K2 is an extraordinarily difficult mountain to climb, the process of generalizing elliptic curves to find a K3 surface is considered an exceedingly difficult math problem.And in Ramanujan’s writing he was relying on this number 1729 in order to arrive at some combination of numbers which could prove that Fermat’s last conjecture could be counter exampled.there are some popular misconceptions regarding ramanujan:Ramanujan recorded the bulk of his results in four notebooks of loose leaf paper (About 4000 theorems)These results written up without any derivations.Since paper was very expensive, He would do most of his work (derivations) on SLATE and transfer just the results to paper.Hence the perception that he was unable to prove his results and simply thought up the final result directly is NOT CORRECTProfessor Bruce C.Berndt of University of Illinois, who worked on Ramanujan note books, stated that “Over the last 40 years, nearly all of Ramanujan’s theorems have been proven right”.Also Mathematicians agreed unanimously on the point that it was not possible for someone to imagine those results without solving / proving.I think I will complete this answer tomorrow, because I feel sleepy: Good Night!Edited in Later:I am extremely sorry for not turning up yesterday to finish the answer I started, because I had gone for an outing to Hoggenakkal in Tamil Nadu.I think I would say something more about the GENIUS before I complete.Well, once G. H. Hardy rated his contemporary mathematicians based on pure talent.Hardy rated himself a score of 25 out of 100,J.E. Littlewood 30, David Hilbert 80 andRamanujan 100 !Hardy also said that Ramanujan’s solutions were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account”Ramanujan’s genius was recognized by TN Government andNow, Tamil Nadu celebrates 22 December as ‘State IT Day’A Stamp was released by the Govt. in 196222nd December started to be celebrated as Ramanujan Day in Govt Arts College, Kumbakonam. Now on 22nd December 2011, Then prime minister Manmohan Singh said that the 125th birth year of Ramanujan will be celebrated as National Mathematics Year and from that year onwards, December 22 is National Mathematics Day.There is a National Symposium On Mathematical Methods and Applications on his name (NSMMA)And there is SASTRA Ramanujan Prize which is given under the auspices of National Mathematics Society and the society for Physics.Let me tell something about the Hardwork of Ramanujan:Once P.C. Mahalanobis, the founder of Indian Statistical Institute visited Ramanujan while in Cambridge and said to him: “ Ramanju, these English Mathematicians say that you are a Genius, A real incomparable Genius.Immediately, showing his thickly black elbow Ramanujan replied, dear friend, everything owes to this elbow.Shocked by the answer, P.C. Asked: How Can it be so?????Ramanujan replied with a smile: “During my childhood days, while using a slate for calculations, repeated erasing used to leave remnants of chalk in it, then I stopped using duster for rubbing.”“This meant that every few minutes I had to rub my slate using my elbow, it means I owe everything to this elbow.”Regarding the spiritual dimension of Ramanujan’s life, all will agree that he was a sort of a mystic, and in fact, Ramanujan was a person with a somewhat shy and quiet dispositionHe was absolutedly a dignified man with pleasant mannersRamanujan credited his success to his family Goddess, Namagiri of Namakkalin fact, He claimed to receive visions of scrolls of complex mathematical content unfolding before his eyes. And we have no idea to contradict his words.And this could be in one way regarded as his Dictom"An equation for me has no meaning, unless it represents a thought of God.”We get amazed the more we know about Ramanujan’s spiritual understanding of many mathematical concepts, I will brief just one.For example, 2n – 1 will denote the primordial GOD.When n is zero, the expression denotes ZERO.He spoke of “ZERO” as the symbol of the absolute (Nirguna – Brahmam) of the extreme monistic school of philosophy)The reality to which no qualities can be attributed,of which no qualities can be there.When n is 1, it denotes UNITY, the Infinite GOD.When n is 2, it denotes TRINITY.When n is 3, it denotes SAPTHA RISHIS and so on.Crazy isn’t it, but all such craziness constituted Ramanujan.He looked “infinity” as the totality of all possibilities which was capable of becoming manifest in reality and which was inexhaustible.According to Ramanujan, The product of infinity and zero would supply the whole set of finite numbers.Each act of creation, could be symbolized as a particular product of infinity and zero, and from each product would emerge a particular individual of which the appropriate symbol was a particular finite number.If you want to go through the life of Srinivasa Ramanujan in its fullness, I humbly refer to you my guide, the book which opened my eyes towards realizing the pearl of Indian Mathematics, and that is:“The man who knew infinity: A life of the Genius Ramanujan”It was written by Robert Kanigel.In that book Kanigel claims some very amazing facts about Ramanujan.Sheer intuitive brilliance coupled to long, hard hours on his slate made up for most of his educational lapse.This ‘poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for next century.S.Chandrasekhar, Indian Astrophysicist, Nobel laureate 1983, told thus:“I think it is fair to say that almost all the mathematicians who reached distinction during the three or four decades following Ramanujan were directly or indirectly inspired by his example.Even those who do not know about Ramanujan’s work are bound to be fascinated by his life.”“The fact that Ramanujan’s early years were spent in a scientifically sterile atmosphere, that his life in India was not without hardships that under circumstances that appeared to most Indians as nothing short of miraculous. He had gone to Cambridge, supported by eminent mathematicians, and had returned to India with very assurance that he would be considered, in time as one of the most original mathematicians of the century.The words of Hardy himelf speak volumes of Ramanujan:“I have to form myself, as I have never really formed before and try to help you to form, some of the reasoned estimate of the most romantic figure in the recent history of mathematics, a man whose career seems full of paradoxes and contradictions, who defies all cannons by which we are accustomed to judge one another andabout whom all of us will probably agree in one judgement only, that he was in some sense a very great mathematician.”Bertrand arthur william russell, British philosopher & mathematician, Nobel laureate and almost contemporary to Ramanujan, stated thus:“I found Hardy and Littlewood in a state of wild excitement because they believe, they have discovered a second Newton, a Hindu Clerk in Madras… He wrote to Hardy telling of some results he has got, which Hardy thinks quite wonderful.”The life of Ramanujan is actually a textbook from which many things could be conceived. Despite the hardship faced by Ramanujan, he rose to such a scientific standing and reputation no Indian has ever enjoyed.It should be enough for youngsters like us to comprehend that if we can work hard with indomitable determination, sheer perseverance and sincere commitment, we too can perhaps soar the way like Srinivasa Ramanujan.Even today in India, Ramanujan cannot get a lectureship in a school / college because he had no degree.Many researchers / Universities will pursue studies / researches on his work but he will have to struggle to get even a teaching job.Even after more than 90 years of the death of Ramanujan, the situation is not very different as far the rigidity of the education system is concerned. Today also a ‘Ramanujan’ has to clear all traditional subjects’ exams to get a degree irrespective of being genius in one or more different subjects.He was offered a chair in India only after becoming a Fellow of the Royal Society.But it is disgraceful that India’s talent has to wait for foreign recognition to get acceptance in India or else immigrate to other places.Many of those won international recognition including noble prizes had no other option but to migrate for opportunities & recognition.(Ex. Karmerkar)The process of this brain drain is still continuing.Here is a pic of Ramanujan with his colleagues in Cambridge University.Talking about certain contributions of Ramanujan which shook me off my feet.As we all know we use the notation P(n) to represent the number of partitions of an integer n. Thus P(4) = 5, similarly, P(7) = 15.I don’t need to explain that If we were to start enumerating the partitions for larger numbers, even for small numbers such as 10 we start seeing that there is a combinatorial explosion! To illustrate this consider P(30) = 5604 and P(50) = 204226 and so on. (btw, partitions can be visualized by Young tableau!).A similar search was on for asymptotic formulae for the partition number P(n) and because of the combinatorial explosion an accurate formula was considered difficult. Ramanujan believed that he could come up with an accurate formula even though it was considered extremely hard, and he came close.One work of Ramanujan (done with G. H. Hardy) is his formula for the number of partitions of a positive integer n, the famous Hardy-Ramanujan Asymptotic Formula for the partition problem. The formula has been used in statistical physics and is also used (first by Niels Bohr) to calculate quantum partition functions of atomic nuclei.The formula he proposed gives a very close value to that of the true value, and it is a mouth-watering feat considering its very pattern less nature.I had written another answer in quora regarding how Ramanujan provided a rapidly converging series as the value of Pi. I will just copy and paste it here.For a long time, the series used for finding the value of Pi was given by the Leibniz-Gregory Series.π = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...But in order to give the value of Pi correctly upto 5 decimal places, this series required around 500000 terms.Now, in the Indian tradition, another formula was given by Nilakantha, a mathematician of Kerala School of Mathematics who lived couple of centuries before Leibniz and the series converged much rapidly.π = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11*12) - 4/(12*13*14) ...And in order to give the value of Pi upto 5 decimal places, this series required only 6 terms. And thats a great thing but which failed to catch the eye of westerners until the nineteenth century.Now, take into consideration all these and what Ramanujan did. Ramanujan simply penned down an infinite series, looking so horrendous, which would be equal to the reciprocal of Pi.And this is the most rapidly converging series ever given for the value of Pi and the algorithm based on this have actually been used in computers.Now the most beautiful factor. In order to have the value of Pi upto 6 decimal places the infinite series of Ramanujan needed only ONE SINGLE TERM.And you take the second term and there you have suddenly the value of Pi upto 11 terms in your hands.I think it speaks something Great, and Ramanujan was indeed Great!!!Ramanujan has done extensive works in finding out highly composite numbers, and he has written down a long list of similar numbers which had more factors than any of the previous number.The highest highly composite number listed by Ramanujan is 6746328388800Having 10080 factorsHe received his degree from the university (later named Ph.D) for his work of highly composite numbers.I would just say another thing which caught my eye and unleashed an array of thoughts.Ramanujan while sick and dying in India, mentioned some very peculiarly behaving functions which mimicked the original moldular functions.The mock theta functions remained a mystery for most part of the last century and only the Great Ono made inroads towards their reality.In fact, no one at the time understood what Ramanujan was talking about.It wasn’t until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,' Ono said.Ono and his colleagues drew on modern mathematical tools that had not been developed before Ramanujan’s death to prove this theory was correct.Ramanujan actually wrote those functions claiming that he saw it in a scroll in the hands of A Goddess.Anyway now they are used to calculate the entropy of Black Holes ( A concept which developed years after his death.)Ono’s team was stunned to find the function could be used today.'No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,' Ono says.Ramanujan’s Intuition Stands OUT!I think, just for a fun I would show the Mock Theta FunctionsNow I think I shoudl mention atleast something about the impact of Ramanujan’s work on statistical physics.For example imagine studying the statistics of a gas made of electrons confined to 2D. You could do something complicated like model the exact positions and momenta of many of electrons along with the force between them. Or you can simplify by imagining that the electrons can only occupy positions on a discrete triangular lattice, and instead of a repulsive force you can make the simple approximation that two electrons aren't allowed to be next to each other.The result is the Hard hexagon model and some work of Ramanujan's appears when you try to model it. Even if it's not physically realistic, these models share characteristics with more realistic physical models and give useful insight.In fact a whole bunch of different identities related to Ramanujan's work can appear when you study these kinds of simple physical models, especially 2-dimensional models. Eg. Hard Hexagon ModelI think I will conclude with a simple assumption of Ramanujan, I think it deserves mention:The mock theta functions which we mentioned earlier looked unlike any known modular forms, but he stated that their outputs would be very similar to those of modular forms when computed for the roots of 1, such as the square root -1. Characteristically, Ramanujan offered neither proof nor explanation for this conclusion.It was only 10 years ago that mathematicians formally defined this other set of functions, now called mock modular forms. But still no one fathomed what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.Ono and his colleagues have exactly computed one of Ramanujan’s mock modular forms for values very close to -1. They discovered that the outputs rapidly balloon to vast, 100-digit negative numbers, while the corresponding modular form balloons in the positive direction.Ono’s team found that if you add the corresponding outputs together, the total approaches 4, a relatively small number. In other words, the difference in the value of the two functions, ignoring their signs, is tiny when computed for -1, just as Ramanujan said. Incredible Intuition !I am just adding some pictures I came across.his notebooks, the last three,His handwritings and works mentioned without calculation:I think I can say nothing more, but if at all someone asks me, I would say if I know!By the way, I have actally spoken nothing regarding the complex mathematical contributions of this great mathematician,even without that I think you are thrilled and that is why, even if the statement is wrong in itself.“ Ramanujan is the greatest Mathematician of all time, atleast I believe so.”

TO PREPARE FOR IIT JEE AT HOME READ THIS ANSWER PROPERLY AND FOLLOW IT:Knowing the ExamUnderstand the structure of the Main exam. The JEE Main lasts three hours and consists of 90 multiple-choice questions. The exam consists of three sections: Physics, Chemistry, and Mathematics. Each section contains 30 questions. All sections are weighed equally.[1]For each question answered correctly, four points are awarded. For each incorrect answer, one point is deducted. No points are awarded or deducted for unanswered questions.Understand the structure of the Advanced exam. The JEE Advanced is structured differently than the main exam. The advanced exam covers the same three topics: Physics, Chemistry, and Mathematics. However, unlike the main exam, the advanced exam is divided into two three-hour long papers, each divided into three sections (one for each topic). The papers are organized as follows:Paper One: Each section contains 10 multiple choice questions with one correct answer, five multiple choice questions with one or more correct answers, and five questions that require the test taker to provide a single-digit answer.Paper Two: Each section contains eight multiple choice questions with one correct answer, eight questions that require responding to a reading passage, and several "matching list"-type questions.Know the topics covered by each test. Though both the JEE Main and JEE Advanced cover the same three subjects (physics, chemistry, and mathematics), the precise topics covered and the difficulty of the individual questions will vary between the two tests. To gain a sense for the topics you may be expected to know for each test, consult the official test syllabi for the Main and Advanced exams, both of which are available in free PDF form from official test resources online.[2][3] Below are just a few examples of the topics you may encounter on the test — these lists are by no means complete or definitive:Physics: Kinematics, laws of motion, gravity, thermodynamics, electromagnetism, optics, electronic devices.Chemistry: States of matter, atomic structure, redox reactions, chemical kinetics, environmental chemistry, periodic groups, basic organic chemistry principles.Mathematics: Quadratic equations, mathematical induction, sequences and series, matrices, integral calculus, differential equations, coordinate geometry.2. Using Study Aids [Using Official Resources]Use official mock tests. The simplest, most effective way to prepare for the JEE is simply to do the test itself. Mock tests are available for free from the official JEE website. These tests mirror the actual JEE in terms of structure, format, and content and can be accessed entirely through your computer — no physical testing materials are required. Completing mock tests gives you the valuable experience of working through the JEE (and, in the process, finding your strengths and weaknesses) in advance of the actual exam.Use question papers from past exams. Another important resource for applicants looking to pass the JEE are the question papers from past tests (freely available on the official JEE website). Unlike the mock tests, which have questions specifically made for them, JEE question papers contain the exact questions included on past exams, making them a very valuable resource.Because the JEE is relatively new (the exam replaced the old IIT-JEE in 2013), only question papers from 2014 are available. However, since the test is offered multiple times per year, as of late 2014, eight papers have been published, offering plenty of practice material. In addition, question papers for the old IIT-JEE (also available online) will cover most of the same topics.Consult the official JEE FAQ for general questions. This article covers most of what a JEE aspirant will need to prepare for the exam, but it's not intended to be a substitute for official JEE test resources. If you're ever unsure about some aspect of the JEE (like, for instance, how to apply, what the eligibility requirements are for public students, and so on), try consulting the JEE FAQ. The FAQ can provide you with the answers to frequently asked questions about the JEE, thus ensuring that you don't have to waste any valuable study time finding the answers elsewhere.Keep up-to-date with official bulletins.Over time, the JEE can (and has) changed. Tests may be rescheduled, results may be re-interpreted, and the topics covered may change. To ensure that you have the absolute best chance of doing well on the JEE, stay up to speed with official JEE bulletins, which are published as they are released on the official JEE website.As an example of the sort of valuable information that may be released in a JEE bulletin, one recent bulletin contained important information on test takers' eligibility for admission to various Indian engineering and architectural programs.Keep in mind the new changes in the JEE Mains Exam. The Central Board of Secondary Education (CBSE) will no longer be responsible for conducting JEE Mains Exam. There is a newly formed authority, National Testing Agency (NTA) which is the in-charge for conducting JEE Mains Examination from 2019 onwards.The exam will be organized twice a year (January and April) in a computer-based mode.The syllabus, exam pattern, language, and fees of the examination will not change.Students can appear either once or twice for the exam.Only the best score of the two will be taken into consideration for admissions.There will be multiple sittings of the exam. A student is free to choose the test dates, centre and schedule within a test period.The highest level of encryption will be used to make the exam more secure. Thus, it will be free from paper-leakage issues and other malpractices.Every candidate will get a unique question paper which will be decided by a software that would randomly pick up questions. This will minimize the chances of cheating.NTA plans to use new age tools like Artificial Intelligence to set questions and prepare answer key.Psychometric Analysis of previous years' tests will be undertaken by the exam conducting authority.JEE Advanced will be conducted only once a year by Indian Institute of Technology (IIT) as was done earlier.3. Using Unofficial ResourcesUse third-party question resources. The official JEE site is generally the most reputable source for test prep materials, but it is far from the only place to find sample questions, practice tests, and other valuable resources. A variety of third-party organizations and agencies also provide JEE test prep materials (some are for free; others cost money). However, since these third parties may not always be reputable or certified, it's important to use discretion and only rely on sources that appear legitimate when studying for the JEE.One great source for JEE test questions is Khan Academy. This relatively well-known academic site offers free educational material on a huge variety of topics and even has a page dedicated specifically to JEE test prep [4]Buy test prep books. In addition to online resources, JEE test prep materials are also available in physical form. Test prep books, brochures, pamphlets, and more are available at academic bookstores. The price (and legitimacy) of these materials can vary — try to choose materials that are officially certified by JEE-administering agencies and contain practice tests, questions from old tests, and so on.It's also a wise idea to pick books that contain full solutions with explanations (and not just answers) for every question — this way, if you don't understand a question, you'll get the luxury of being walked through the question step-by-step, rather than having to piece the solution together based off the final answer.Review your notes from school. If you've been a diligent student, you may have access to great test-prep resources and not even realize it! Dig up your notes from physics, chemistry, and mathematics classes you've attended and review them, taking time to highlight important topics for further review. If you have access to old problems, consider going through some of these as well for extra practice.Some students may find it useful to read old textbooks directly — if this is the case for you, feel free to. However, for many, the "dense" way material is presented in many textbooks can make it almost impenetrable, so this may not be a great use of your test prep time.4. Using Your Study Time WiselyStart as early as possible. When it comes to preparing for the JEE, the earlier you start, the better. Studying for the JEE is a serious undertaking, especially if you plan on taking the JEE Advanced. It's also one that can have a significant impact on your professional future — a great score on the JEE can make it much easier to get into the engineering program of your choosing. For these reasons, some people choose to start studying years before they'll need to actually take the JEE. Though this probably isn't necessary if you've been attentive to your studies, for the best score, you will probably want to begin as early as practical — at least a few months before your test date.Spend the most time studying your weakest topics. As you study for the JEE, you'll want to devote some time to every topic, even if you're already confident that you know some of them very well. However, to get the best score possible, you'll want to devote the majority of your time to the topics that you're not confident in. Doing this ensures you get the biggest improvement possible from your studying effort.If you're not sure how to allocate your time, try reviewing your grades from school — spend your most time studying the subjects that you get the poorest marks in.Eliminate your personal distractions as you study. In the months before the JEE, you want to make the most of your time — you don't want to waste an hour (or more) fooling around for every hour you spend studying. To avoid distractions like TV, video games, and other forms of digital entertainment, remove them from your life temporarily. For instance, if you're having a hard time giving up your video games, you may want to try leaving your game system at a friend's house until the test is over.Try to use the internet only for study purposes. Don't waste your study time on games or social networking until the exams are over. If you can't seem to overcome these online distractions, try downloading and installing a productivity app (most browsers will have these available for free in the browser store).Time yourself as you take practice tests. When you practice individual problems in preparation for the JEE, a good rule of thumb is to take as long as you need to fully understand the problem and answer it correctly. However, when you take entire JEE practice tests, it's a smart idea to give yourself the same 180-minute time limit you would normally have to finish the test. Doing prepares you to account for the time limit when it will actually matter.You don't necessarily need to be able to complete the entire test within the time limit the first time you try to do so, but you should work to increase your speed so that you're able to finish the whole test in 180 minutes (with as few questions skipped as possible) by the date of the test.Take care of your physical needs on test day. Past a certain point, additional studying prior to the JEE can actually be harmful. If you have to give up eating or sleeping properly in the days prior to the JEE to squeeze in last-minute studying, you're probably hurting your chances of getting the best grade that you can. Neglecting these basic physical functions can leave you drowsy and distracted on the day of the exam, making it tricky or even impossible to do your best. Take the time to relax, eat normally, and get plenty of sleep in the days before your test — if you've been studying all along, it's almost certainly the smartest thing to do.This advice isn't unique to the JEE. Neglecting your physical needs (especially sleep) before any test has been demonstrated to lower your score on average.[5]All the best!!

I'll speak up for Caltech here.Going through undergrad at Caltech is the hardest thing you'll ever do.Before I can talk about anything else, you have to understand what I mean by this.Caltech is a place that was built up to take the best scientific minds in the country and push them harder, faster, and further than they'd ever experienced before. It manages this through a couple key points:There are almost no introductory classes. The 'normal' class track for most majors has you taking graduate level courses starting in your sophomore or junior year.The core curriculum requirement is incredible. Every undergrad at Caltech is required to take courses in analysis, multivariable calculus, linear algebra, differential equations, probability and statistics, classical mechanics, special relativity, electricity and magnetism, waves and optics, thermodynamics, quantum mechanics, general chemistry, physical and organic chemistry, chemistry lab, a second lab class chosen from the likes of nanofabrication labs, physics labs, etc, the biology and biophysics of viruses, and a 'breadth' or 'menu' course chosen from the likes of introductory astronomy, geology, information science, energy science, etc. Everyone takes all of these. No matter your major. Yes, even the premeds have to pass quantum mechanics.You take many, many classes. Taking 5-6 courses simultaneously is considered normal. This doesn't count any 'small' course listings like playing for the athletic teams or somesuch. No, we're talking 5-6 full-blown, hardcore science courses. Taking anything less, even just 4 courses, makes it difficult to remain a full-time student, and difficult to fulfill all the requirements you need in order to graduate on time. On the other hand, many students find themselves taking 7 courses at once in some terms.The classes move extremely quickly. Some time ago, Caltech moved to a quarter system where each quarter lasts 10 weeks. Rather than simply teach less material than a corresponding semester-long course, the professors adopted the policy of just accelerating the coursework so that each quarter-long course covers a full semester's worth of material.Add onto all of this what can be a somewhat insular social environment that can be as challenging to deal with as your courses, and you can begin to understand what I'm talking about.To put things into a Silicon Valley perspective, when I came to Mountain View to start a software startup, I asked around to a lot of the alumni contacts I knew for advice. One thing that was often repeated was the warning that "I'd like to say that starting a startup will be the hardest thing you'll ever do, but you were an undergrad at Caltech, so I can't. Instead, it'll be the second hardest thing you'll ever do."Now for the rest of the experience:Like many world class universities, the faculty are amazing. You take courses from people who literally wrote the book in their fields. I won't belabor this point because by now you've seen it reiterated many times in the other answers to this question, but it's pretty neat, and worth mentioning once.The laboratory access is unparalleled. It is literally as easy to get a spot in a world-class lab as walking up to a professor after class and expressing your interest. This includes research gigs at national labs, JPL, and associated research facilities. Almost every single student does some form of research work while at Caltech. Most do research work over the summer—when no classes are offered—but many continue their laboratory involvement full time during the school year, on top of the 5-6 classes they have to take as a full-time student.The Caltech Honor Code is sacred.No member of the Caltech community shall take unfair advantage of any other member of the Caltech community.Every Techer knows those words by heart. The attitude of the honor code permeates the school, and every interaction within it. It is taken so seriously that cheating is almost unheard of, despite take-home midterms and finals (more on this later), and when cheating does happen, investigation and punishment of any offense is left to the undergrads. Specifically, there is a group in the student government called the Board of Control (abbreviated BoC), which is responsible for policing academic dishonesty. Their decisions, though reviewed by the dean of students, are almost always upheld, and may include 'corrective' measures that range from nullifying a student's grade on an offending exam, to nullifying a student's grade in a class, to placing a student on involuntary leave or even expelling a student outright from the Institute.Advantages of the seriousness with which the Caltech community takes into mind the honor code include the ease with which students can gain personal keys to buildings and laboratories on campus, and extreme levels of comfort and safety around your fellow students. Though it's not advised, you can basically leave the door to your room open for hours without being personally present, and expect to find nothing missing or misplaced upon your return.It is literally a violation of Institute policy to administer a proctored exam. Midterms and finals are take-home, almost without exception. The only time I ever had an in-class final was for a humanities class where the professor didn't want us to spend too much time worrying about the final paper. He walked in the door, wrote the prompt on the chalkboard, told us we had two hours to write and after that, he'd be back to pick up the papers, and walked right back out the door again.Take-home exams include specified time and resource limits. For example, they might say "This exam must be taken in four hours, in one sitting, and you may only reference your own hand-written course notes." or "This exam may be taken over the course of six hours, with a single thirty-minute break not counting against that time limit taken at any time. This exam is considered closed-book, and you may not reference any outside materials." The worst exams, though, have descriptions that go like this "This is an 'infinite-time' exam. You may work on this exam throughout the entirety of finals week, but must turn it in at 5pm on the last day of the week. You may reference anything you like, including any textbooks, Google, or other internet resources, but you may not discuss problems on this exam with anyone else." Infinite-time, open-Google exams are legendary and terrible, because the more resources the professor has made available to you, the more you can be sure that those resources won't help you. It's not uncommon for professors to put open research problems in the field on exams like this.Another note about Caltech exams is that often, when professors run out of time to teach additional topics in their courses, they'll include those topics on the final exam anyway, expecting students to use the open-book policy to learn the topics from the textbook on the fly, during the exam, and to then answer difficult questions relating to them.Caltech requires its students to take a great number of humanities courses. Little known in the outside world, Caltech has a significant (12-courses, which averages to one every quarter) requirement in the Humanities and Social Sciences that every student must complete in order to graduate. While you have great flexibility in choosing the individual courses you take, you are required to spread them out among several broad categories. Courses eligible for fulfilling this requirement include—beyond the expected literature, foreign language, history and philosophy offerings—those offered in anthropology, business and economic management, economics, law, and political science. It should be noted that many of the courses offered in these latter categories have a particularly 'Caltech' approach, often involving significant levels of mathematical analysis, e.g., game theory in economics courses, or options pricing models in related business classes. Despite the unexpected nature of this requirement, many of the best classes I ever took at Caltech were humanities courses.Years of the Caltech course load give you an incredible ability to focus and to learn new fields extremely quickly. Like I mentioned earlier, there are very few introductory classes. Most of the time, you're dropped into courses alongside graduate students in the relevant fields. The difference is that all the grad students have had lower-level, introductory courses at their previous institutions. The undergrads? Not so much. A consequence of this, and of the often 60+ hours a week of problem sets you have to deal with, is that the only way to survive is to develop an incredible ability to focus on the tasks at hand in conjunction with the ability to rapidly learn new fields. The core curriculum helps immensely here, because through it, every student has some basic familiarity with almost every concept in science.To put it another way, at Caltech, you spend almost every single day for four (or five, or six, or seven) years straight facing problems that you don't know how to solve. The idea of being faced with a problem that you don't understand, then, isn't a scary thing anymore, and instead becomes familiar. Since giving up is not an option, through such repeated exposure to problems you don't understand you develop a method of dealing with them. You learn how to break unknown problems up into parts, to categorize and classify them, to make powerful analogies to situations you are already familiar with, to learn to use new techniques and methods of thought, and to invent a hundred crazy approaches in a row when nothing else seems to work. Problems that you don't, initially, have any clue how to solve are par for the course, for every course, for every problem set.There is a special kind of intelligence among the undergrads at Caltech. I hope the idea that Caltech undergrads are extremely focused on scientific fields will come as no shock to anyone reading this. I should stress, though, that that same focus does not imply a corresponding lack of interest in non-scientific fields. Like most schools, students at Caltech have a wide variety of interests, and like most world-renowned schools, students at Caltech take their outside interests very seriously. The result, though, is curious in a way that I suspect is probably only really duplicated at MIT. You see, at Caltech, like many other schools discussed in this question, you often get into fascinating discussions with your fellow students about everything from political events to philosophy to popular culture. However, unlike most other schools discussed in this question, when debate occurs at Caltech, it is a very particular kind of debate indeed. At Caltech, real-world evidence and logical thought processes are of paramount importance in a way that can only be true at a place with such a singular focus on science. Blind conjecture, unfounded assertions, emotional exhortations, or contradictory beliefs will get hounded out faster than a fox at a beagle convention. In many cases, it's exhilarating. In some, it's annoying. But it always keeps you on your toes.The social atmosphere:There are enough details that go into this to make it worth its own section in my answer.The house system.Caltech has no dorms and no fraternities or sororities. Instead, there is the house system. There are eight houses, each of which contains between about 70 and 120 students. The houses have membership rules similar to frats, and select new members from among the freshmen during a week-long event at the beginning of each school year called Rotation. Each house is self-governing, extremely close knit and has its own personality, traditions, and quirks. A recent student experience trip conducted by the Caltech student government found that Caltech's house system promoted a greater degree of interaction between students of different years than was commonly found anywhere else among the other schools toured across the nation.Each house organizes social events for its members, sports (and other) challenges against other houses, and parties for the entire campus. It's often said that Caltech is very much like Harry Potter, except we have eight houses instead of four, and no talking hat.To get an idea of just how important the houses are at Caltech, consider that alongside class-year reunions, Caltech's alumni association organizes House-specific reunions for each of the eight houses.Caltech parties are legendary. Take two parts brilliant engineers, five parts stressed-out students needing a release, three parts wild and crazy ideas, and one part easy access to money and construction equipment, and what do you get? Students spending months building, painting, and decorating parties for a single wild night. Past parties have included flooded courtyards and floating dance floors, snow machines and giant submarines, huge pyramids, rope bridge entranceways extending out of roof-level stairwell windows, programmable LED nets, fifty feet on a side, underground passages, and more. It's unbelievable.Nevertheless, Caltech is extremely emotionally challenging. Years on end of exposure to the pressure cooker environment, to incredibly challenging work, to all-nighter after all-nighter—the most depressing thing is when your all-nighters are regularly scheduled every week by the dictates of your coursework—to, in a nutshell, an environment where your best is never good enough, because nothing is ever good enough, and you're running as fast as you can just to barely be able to keep up with everything and you're desperately hoping that nothing goes even the slightest bit badly—like getting sick for a weekend, or, god forbid, during the week—because then you'll be forced to play catch-up, and it's almost impossible to catch up once you've fallen behind, and it's a victory when you get six hours of sleep one night because that's the most you'll sleep this week until Saturday, and you've just gotten your midterms back, but you can't relax because you've got finals in three weeks, and you're trying your hardest at your sports practice, but it's not going so well because you're sluggish on the court because who has reflexes worth a damn when you're lucky to average five hours of sleep a night, and the prof whose lab you're working in expects new experimental results on Monday, and your friend is having a breakdown because of relationship issues that you're hearing no end of, but you want to help because they're your friend, and another friend you know is in a serious depression because god damn, the stress level is through the roof, and how the hell are you supposed to finish soldering your project together at five in the morning when your hands are shaking and your vision is blurring, and you can hardly keep your eyes open anymore, and you know that you'll be sick to your stomach all day tomorrow because that's what always happens after nights like this.During my time at Caltech, I knew more than a dozen people who spent time at the local mental health clinic's suicide watch ward. I would be surprised if any Caltech undergrad never had a friend end up there.Finally, I should mention that the small size of the school opens up many opportunities. Because the school's population is so small (only about 850 undergrads) and so selective, the faculty and administration are incredibly accessible, and treat the students with a great deal of respect. It's not unusual for a student to be able to schedule a same-day sit down meeting with any member of Caltech's administration or faculty. Further, students sit on almost every Institute committee, from the search committees for new vice presidents of the institute to the freshman admissions committee and beyond. It's incredibly easy to make connections to members of the faculty and the administration, and I know many fellow undergrads who have found those connections to be absolutely invaluable.In conclusion, while I haven't discussed every detail and aspect of attending Caltech as an undergrad, I believe I've hit on the most important points. I've left out innumerable crazy stories and weird traditions (throwing liquid-nitrogen-frozen pumpkins off of the roof of a ten story building on Halloween night, anyone?), as well as some of the finer details of the way the school runs, but I hope I've been able to impart some visceral understanding of what the school is like for most of its students.