First of all, i'd like to apologize to all those who managed to read the part-1 and "actually" waited for part-2. On my part, i can only say that i was quite busy with my life in IIT. Well, without wasting any further time in discussing crap things, let's come straight to the point. So, we were done with 7 shortcuts, here are the remaining few which i remember-

Here, the sum of 1 natural number is 1. Now, if you put n=1 in the options, we get;

Now, if you actually start doing the maths of it, you will find yourself in a trouble of inequalities. So better think of an alternative. As we are given necessary conditions for with

Similarly, in questions where you are given random inclinations of plane (alpha,beta,etc), see what will happen if the inclination was zero/90. Now put alpha/beta/whatever equal to zero or 90 in the answer and see which of them satisfies the condition. Similarly, for finding moment of inertia about a random axis, same can be appllied.Try this one yourself. Example: Find M.O.I of a rod along an axis at theta degrees from its length passing through the centre.

Moreover, never go to the exam centre with any book or anything. The only thing you should be carrying is your admit card and a pencil box with your stationery. And if you feel low while studying, here are some songs that will help lift you up. Put them in your cellphone/ipod and listen over on

Live like you're dying-Kris allen **8) Find for n-terms:**There are perhaps the easiest kind of questions in maths. Generally, the**n**th term or sum or product of n-terms is asked. What you can simply do is put the value of n=1,2,3 in the given options and compare with what value will come for 1,2 or 3 terms by simple calculation. Mostly, the answer comes with n=1 or 2. The maximum number of trials required in such questions is 3. If it goes beyond 3, then the question is a high level one and it's better to leave it alone. Example: Sum of n natural numbers (1+2+3+....+n) is**(a)**n(n-1)/2;**(b)**n(n+1)/2;**(c)**n(n+2)/3;**(d)**(n+1)(n-1);Here, the sum of 1 natural number is 1. Now, if you put n=1 in the options, we get;

**(a)**=0;**(b)**=1;**(c)**=1;**(d)**=0; Hence, options**(a)**and**(d)**can be ruled out. For n=2, the actual answer is (1+2=**3**). On putting n=2, we get**(b)**=3;**(c)**=8/3. Hence, only option-**(b)**is the correct answer. Similarly, with some practice, you can easily learn how to apply this kind of logic in questions.**9) Generalize the question:**This is one of those favorite derivation types questions given in JEE. They will give you a complex orientation and ask you to find one of the variable.what you have to do is assume an orientation such that two or more of the arbitary values go to zero/one/some easy value and then check the options again. Example: suppose for positive real values, it is given that :m

^{3}x

^{4}=n

^{3}y

^{4}and m

^{2}<n

^{2},then

**(a)**m

^{3}x

^{2}>n

^{3}y

^{2};

**(b)**m

^{3}<y

^{4};

**(c)**m

^{3}x

^{2}<n

^{3}y

^{2};

**(d)**m

^{3}>y

^{4}

**m**and**n,**so lets assume m=2;x=3;n=3**.**Thus, you will get y as fourth root of 24**which you can approximate as square root of 5(coz****5x5=25**)**.**Now root of 5 is 2.2. For these questions you have to be good at approximating values which is not a big ask (atleast its more natural than remembering all identities). Now put these values in the options. You will easily see that on cancelling the**"3"**in the options wherever possible, the only option that still stands as correct is option**(b)**which is the answer.Similarly, in questions where you are given random inclinations of plane (alpha,beta,etc), see what will happen if the inclination was zero/90. Now put alpha/beta/whatever equal to zero or 90 in the answer and see which of them satisfies the condition. Similarly, for finding moment of inertia about a random axis, same can be appllied.Try this one yourself. Example: Find M.O.I of a rod along an axis at theta degrees from its length passing through the centre.

**(a)**ML

^{2}sin

^{2}Ө/12;

**(b)**ML

^{2}cos

^{2}Ө/12;

**(c)**ML

^{2}sinӨcos

^{2}Ө/12;

**(d)**ML

^{2}sin

^{2}ӨcosӨ/12

**SOLUTION:**Here, we clearly know that M.O.I of a rod along its length is zero. So at Ө=0; M.O.I=0. On putting Ө=0 in options,**(a),(c)**and**(d)**become zero. Also M.O.I of a rod perpendicular to its axis i.e. Ө=90 is ML^{2}/12. Now, on putting Ө=90, only**option(a)**gives ML^{2}/12. Rest all become zero. Simple!! Isn't it??**10) Modern Physics (atom,nuclei,radiation,etc):**Now this is one topic you would not want to lose marks on. This topic accounts for roughly 20-25 marks in IIT-JEE and you won't need more than a day to expertise this topic even if you start from scratch. If you can't expertise, atleast cram all the formulae related to modern physics.**YOU SIMPLY CAN'T LET THE QUESTIONS FROM THIS TOPIC GO AWAY FROM YOU.**If you atleast remember all the formulae, you can devise something even in the exam ahll to find the correct option but please DON'T LEAVE IT. Its study requires less than one-tenth of the time required to study "Mechanics" and still it provides marks- 10 times than "Mechanics".**STRANGE BUT TRUE!****11) Co-ordinate geometry:**This is one area where even a raw but approximate diagram may work in some questions of finding radius, area, equations,etc. Simply draw a diagram according to scale and try to find the required thing. It may seem trivial but it works in many situations. What's the hesitaion in trying something to get to the answer when you don't know the concept? :-p**12) Kinematics, trigonometry:**These are the two least weightage topics in JEE. Try to do them as late as possible. It won't even hurt if you leave these topics. They are meant to take up huge volumes of your time and have maximum 2-3 questions in JEE. In the same amount of time, you can score 20-25 marks by studying other topics. YES! IT-IS-TRUE! One may argue that trigonometric basics are used at lots of places elsewhere. My answer is that what you know about trigonometry, by default, is enough to solve the main questions. The tricky ones require use of some identity which only the geekiest of nerds will have idea about. So its better off to leave these topics and concentrate on other areas.**13) Chapter-1 (physics):**Remember it? When you enter 11th standard, you have the first chapter about measurements and all which no one cares about. I don't know why no coaching institute pays importance to it. But, this chapter is one easy piece of cherry. Read it thoroughly. You get 3 questions from it about dimensions,maximum error and approximation. If you are not able to understand it from the book, read all the questions from your study material about it. On looking up the answer key, you yourself will eventually figure out the ways to get to the answer of these problems. Remember, on the answer-sheet, only the answer is important. No one cares about the way to get to it. This chapter is just freely distributed marks.**14) NCERT is GOD/GITA/QURAN/BIBLE/WHATEVER:**Even my teachers used to say the same when i was in 12th and even i never paid attention to it. But, today i know they said the truth. NCERT is the most precise book esp. in case of CHEMISTRY. In physics and maths, you may find deviations but every question of Chemistry in IIT-JEE is taken from the NCERT book. Read or maybe cram the whole of NCERT (chemistry especially). Most importantly, questions in inorganic chemistry are**directly lifted lines**from the NCERT.**15) Mind over heart:**This happens with the most of us. We see a question in exam and our heart says that the answer is something whereas the mind says something else. Always, go with the mind. The IIT-JEE is meant to test 'intelligence' of over 5 lakh students, not to simply test if something new strikes you during the exam. So, let only the mind solve the questions and let the heart only keep up your spirit. The reverse leads to disaster!**16) Confidence:**Whatever happens, this is the most important thing needed during the preparation and exam. Let your spirits always stay high. Remember this fact- " The person writing all this (Dhawal) had only confidence with him. His concepts were zero but still i managed to clear JEE because he believed in himself." And i am not being modest or anything. Neither am i thinking low of myself. I am simply saying the truth in your as well as my face. So, If i can.....anyone can!!Moreover, never go to the exam centre with any book or anything. The only thing you should be carrying is your admit card and a pencil box with your stationery. And if you feel low while studying, here are some songs that will help lift you up. Put them in your cellphone/ipod and listen over on

**earphones.**I believe it will help you.Firework-Katy Perry

Lose Yourself-Eminem

Remember the name- Fort minor

Someday- Flipsyde

Who says- Selena Gomez (esp for girls)

ALL THE BEST FOR YOUR J.E.E..!!! Good luck..!!! Hope i helped you in some way.

P.S: If you are doing engineering just for the namesake of it, then you are committing a grave mistake. All you will end up with is an irritated you. If you actually are interested in solving question by such methods as i suggested, the C.A.T is the exam for you. In C.A.T coaching, you are officially taught all these methods. :p And, if you have to give C.A.T in the end, then why waste 4 years on a degree that is almost rendered meaningless after M.B.A. So my final word is that-

"Do engineering if only you are really interested in it. Else please don't waste your life on engineering. Rest is all upto you."