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PDF Editor FAQ

Can you score 170 plus in the MHT CET with this preparation?

Thanks for A2A.CET score of 170+ is hard to achieve. You need to be well known of the portion and weightage given to each chapter in PCM.Marvel publication is really good for Maths MCQs. Do 20 questions from each chapter of maths given in Marvel. That much is sufficient. If you feel you are not yet confident enough in Calculus then do some extra problems from any other publication.I had used Vidyabhartee Publications for Chemistry. This book is well equipped with all the reactions of organic and formulae and shortcuts you need for inorganic. All you need for scoring in chemistry is good memory!Arihant Publication is enough for Physics. Try to solve 30 problems from each chapter and write down formulae of all the chapters on 3-4 sheets. You need to read these 4 pages daily.One tip - Don't do a subject for more than 4 hours continuously. Doing so will make you fatigue. Take proper healthy food and take sleep for at least 6 hrs. Don't take too much tension. You will get a score you deserve.I followed the same schedule as above and got 175/200 in MHT-CET 2012. I was scoring in the range of 160- 165 in April when I was appearing for the practice tests in Crash course.All the Best.

What are some things that mathematics students know, but others don't?

I was waiting that someone will ask it. Was sick of same question about computer guys, and programmers.Let me tell you some-[math] \pi \neq 22/7 [/math]0.999999.......=1The Largest known prime number till this date is [math] 2^{57885161}-1 [/math]. It has [math] 17,425,170 [/math] digits. It is a Mersenne prime'Balls' can be square too.Everything you can do with ruler and compass, you can do with compass alone. For more info read this- Geometric construction with the compass aloneThe most famous theorem of mathematics- Pythagorean theorem- whose NCERT proof troubles school kids most, has more than 500 proofs, may be more than 1000's. Eli Maor wrote a book in which he showed 367 proofs that were distinct enough to bother writing about separately. " (The Pythagorean Theorem)"Yes, 1>0 needs a proof.​​​[math] 0 [/math] can be equal to [math] 2 [/math], if you work in field of characterstic 2 i.e. [math] \mathbb{Z}_2 [/math].Jordan Curve Theorem- It is a very tough theorem to prove that every simple closed curve divides a region into two parts, "interior" and "exterior".​​​​A mathematician Kurt Godel has actually proved that God exist!!The Proof-Gödel's ontological proofA shape with finite volume must have finite surface area- FalseGabriel's Horn is an example.There are more rational numbers than there are integers- False[math] i^i [/math] is real number.​​​​The Fibonacci sequence is encoded in the number 1/89- ( 1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 ...)Too much beauty in one pic..In a room of just 23 people there’s a 50% chance that two people have the same birthday.​[math] 1+1/2+1/4+1/8+ \ldots \ldots =2 [/math]Joke based on this- Infinitely many mathematicians walk into a bar. The first says, "I'll have a beer." The second says, "I'll have half a beer." The third says, "I'll have a quarter of a beer." The barman pulls out just two beers. The mathematicians are all like, "That's all you're giving us? How drunk do you expect us to get on that?" The bartender says, "Come on guys. Know your limits.[math] 1+1/2+1/3+1/4+ \ldots \ldots =\infty [/math]Joke base on this- An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third orders a third of a beer. The bartender bellows, "Get the hell out of here, are you trying to ruin me?"A pizza that has radius “z” and height “a” has volume Pi × z × z × a.If you shuffle a pack of cards properly, chances are that exact order has never been seen before in the whole history of the universe.Explanation- A deck of 52 cards can be ordered in [math] 52! = 52 \times 51 \times 50 \times...\times 2 \times 1 [/math] ways. But 52! is a very large number: larger than[math] 8 \times 10^{67} [/math].How big is this number? Well, someone shuffling a deck of cards once per second since the beginning of the universe (believed to be about 14 billion years ago) would not have shuffled the deck more than [math] 10^{18} [/math] times.Zero is even number.Three Interesting Theorems-The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color.Brouwer’s Fixed Point Theorem (implication) says that if you take two sheets of paper, one lying directly above the other. If you crumple the top sheet (do not rip or tear the sheet), and place it on top of the other sheet, then there must be at least one point on the top sheet that is directly above the corresponding point on the bottom sheet! Do you believe that?Hairy Ball Theorem (Real life implication)- It states that given a ball with hairs all over it, it is impossible to comb the hairs continuously and have all the hairs lay flat. Some hair must be sticking straight up!​​​​It took Russell and Whitehead several hundred pages to prove that 1+1=2 in Principia Mathematica.Divisibility by 7-Remove the last digit, double it, subtract it from the truncated original number and if the result is a multiple of seven, then so is the original number, keep repeating till number is small enough.Random walk theory- A result by Polya states that in one or two dimension, a random walker returns to the origin infinitely many times but only a finite number of times in dimension 3 (or greater).Thus they say- "A drunk ant or a drunk man will always reach home but a drunk bird might not!Mathematician exclusive jokes-"The B in Benoît B. Mandelbrot stand for Benoît B. Mandelbrot."(If you know a little about Fractals)My Favourite- "A comathematician is a device for turning cotheorems into ffee." (Hint look up Paul Erdos quotes)."I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. "No" he replied, "it is a very interesting number. It's the smallest number expressible as the product of 7 and 2 in two different ways."-Hint- Ramanujan's most famous story.Prof: "Give an example of a vector space."Student: "V"Why did the mathematician name his dog "Cauchy"? Because he left a residue at every pole. :PThe primary reason Bourbaki stopped writing books was the realization that Lang was one single person."Let epsilon<0."[math] \int 1/cabin \ d(cabin)= Houseboat [/math] {Don't forget the constant C (sea)}[EDIT]36. Wine/water mixing problem-In the wine/water mixing problem, one starts with two barrels, one holding wine and the other an equal volume of water. A cup of wine is taken from the wine barrel and added to the water. A cup of the wine/water mixture is then returned to the wine barrel, so that the volumes in the barrels are again equal. The question is then posed—which of the two mixtures is purer?Any Guesses?Answer- Both mixtures will be of equal purity.Yes it is a math (logic) problem. Here is the solution-37. Frobenius Coin Problem- You must have done a puzzle like " the largest amount that cannot be obtained using only coins of 3 and 5 units", Right? Answer here is 7 units. Answer to this type of problems is called Frobenius number.For the case of two denominations , say, a units and b units where a and b has no common factors other than one, there is a formula to get the answer i.e. Frobenius number, which is N= ab-a-b.But there is no formula for case with three or more denominations, but algorithms exist.

How should I study to ensure a top 50 rank in the JEE Advanced in one year? How many hours should I devote? I'm only an average student but, I am ready to sacrifice anything.

Your last line took my ❤️. If you are willing to sacrifice, then trust me you can totally do it.One of my friend cracked Rank 18 in just one year of preparation. I myself got under 150 in less than 1 year in JEE advanced.This is what I did.(1) Go through the concepts thoroughly, solve at least one module or book completely along with theory of each chapters. If talk about Maths, do necessarily solve bansal sheet and Some standard textbooksYou have 12 months and approx 30 chapters in each subject, so you must cover at least 3 chapters monthly. Initially you can plan to cover 4 chapters monthly and later reduce so that you can get time to revise.(2) After completing any chapters, do revise all the theory points in your mind. It's a very important practice and it will connect you chapter as a whole.(3) Follow a routine of solving minimum 100 problems everyday in all three subjects combined. Try not to leave any problem unsolved. Gather multiple solutions if possible.(4) If any part of syllabus bother you too much, I would suggest leave that for later stages.(5) Do write a test at least once in 20 days and improve your pressure handling skills.(6) Build your own strategy to attempt question paper.(7) Practice practice practice is the solution to your every problem in this year.All the best.PS: To get more clarity on the strategy, you can read my other answers.

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