Wednesday 26 February 2014

Thermal Physics... Hot topic in JEE

The topic mentioned in the heading is just too damn heavy for JEE - Yes, heavy in terms of it's weightage in JEE.
To get a feel of how important it is, pick up the past year JEE papers. Each JEE paper contains at least 5-10 problems from thermal physics. So better prepare it well.

Basics : This include the topics of thermal expansion, thermal stress etc. They are simple topics and must be done if you have solved a few standard problems. The problems of expansion involving liquids inside a container are important and easy. You may be asked to measure the new length measured by the scale when scale and the object(whose length is to be measured), both expand. Such problems are easy and interesting and must be done in a single shot.

Heat Transfer : Slightly important topic. I remember there was a question regarding calculation of equivalent thermal conductivity in JEE 2013. Although JEE mentions heat conduction in one dimension, you still may try heat conduction through a cylinder (2 dimensions) and heat conduction through a sphere (3 dimensions) for Olympiads. Laws of radiation and Newton's laws of cooling are important. You should learn the definitions of emissivity/emmisive power/absorptivity/etc by heart. I remember I used to mix these definitions. Pick up HC Verma and learn the definitions in that book. Kirchoff's law, Wein's displacement law, Stefan's law etc are important and easy to grasp topics.

Thermodynamics : Here comes the big gun. This topic is extremely important because having a grip on this will help you not only in physics but also in chemistry. Learn the specific heat capacities of various gases at constant pressure and constant volume. They won't be given in exam. Learn the definitions of various processes, most important one being isotropic process. Solve a large number of problems from thermodynamics of ideal gas. A word of caution here. Make sure that you don't mix up the physics and chemistry conventions of First law of thermodynamics. They take work done as negative in chemistry but not in physics.

Books : HC Verma, Arihant. These two books are more than enough.


Revision : Revision packages like FIITJEE GMP, resonance Rank booster or the one provided by your coaching.

Final word Practice a number of problems from the First law of thermodynamics. It's really really important from the point of JEE. Also, it is important from the point of Indian National Physics Olympiad. I remember having a 13 mark question in INPhO 2013 from a combination of SHM and Adiabatic process. So better learn the formulas of Work done, Heat and change in internal energy in all the processes.
Cheers

Saturday 22 February 2014

Calculus - Awesome Mathematics

This is going to be a long one. Better grab something to eat.

Calculus has remained my favourite topic since JEE. It's the best, the most logical and the most beautiful topic for me. It has it's own beauty. It's a mixture of everything - co-ordinate geometry, algebra, vectors and what not. It's because of my interest in calculus that I performed good in our calculus course. It's extremely important from the point of engineering.
Coming back to JEE, 
Here is a chapter wise discussion of JEE calculus.

Functions : forms the framework of calculus. Understand this concept well otherwise studying calculus will be a tough time for you. Common questions are :

  • finding domain/range of a given function : students commit silly mistake here
  • given a domain and range, finding the number of one-one, onto, etc functions
  • plotting graph and finding number of intersection points of 2 or more functions
study this chapter well, especially graph plotting. It's going to help you a lot.
Practice a number of problems of finding domain/range. There are tricks like :

  • no negative number inside a square root.
  • no division by zero
  • no negative number zero inside log
  • base of log is not equal to 1 etc etc.
They expect you to know these basics. A good practice is to cross check your answer from the options available.

Limits : Most important part. Entire calculus is based on finding limit of a function. L'Hopital's rule is extremely important. Apply it as much as you can. You might also give a try to series expansion but I avoided it because most questions of series expansion can be solved if you are good at L'Hopital's rule. So, I never needed it. However, it is advisable to remember the exponential and logarithmic series.
Questions from this chapter are usually straight forward and simple. You just have to figure out the zero by zero form or the infinity by infinity form and apply L'Hopital's rule.
The variety of questions is large.

Continuity : another important topic. This chapter can be solved if you are accurate and quick at drawing graphs of functions. Continuous functions have many interesting and important properties like "intermediate value property", invertibility etc. Understand them and apply them.

Differentiation : One of the easiest chapter. Doesn't need much effort. Learn the formulas of differentiation - quotient rule, product rule, chain rule, implicit differentiation, differentiation of exponential and logarithmic functions, higher order derivatives. Practice enough questions.

Application of derivatives : Most-most-most important chapter because maximum number of questions are asked from this topic. Rolle's theorem, Lagrange's mean value theorem, concept of maxima-minima, increasing and decreasing functions, inflexion points, etc are really really important. Practice as many questions as you can from these topics. Be prepared to see maximum questions in JEE from this topic. If you are weak at it, then better do something otherwise you will face trouble. This chapter basically is the application of all that you studied in the previous chapters and JEE is all about applying concepts.

Integration : Relatively easy chapter. You won't find many questions in JEE from indefinite integrals. There are a number of formulas to be remembered from this chapter. The formulas are extremely important because you will sometimes need them in definite integration.

Definite integrals : most important topic of integral calculus. There will be a good number of questions from this chapter. Most questions will be based on the properties of definite integrals rather than just applying fundamental theorem of calculus to a definite integral.
Practice enough questions from this topic.

Differential equations : A relatively simple and interesting chapter. Need a good amount of practice and some memorizing skills. Learn the known methods of solving the standard differential equations and you will enjoy this topic.

Books : Arihant differential calculus, Arihant integral calculus (Both by Amit M. Agarwal) are the best books for this topic. They will cover almost everything (except one topic - inflexion points which you may cover from somewhere else). Solve all the subjective and objective problems of the book. You may choose to ignore the extremely long ones because they are meant for olympiads etc.

Revision : Revise from the standard revision packages in the market. FIITJEE GMP or Resonance rank booster or the one provided by your coaching will be sufficient.

Final word : Calculus needs a lot of cramming. There are a number of standard methods and techniques that you are expected to remember. You won't derive the formulas in exam. Just understand them at home and then learn them by heart.
Practice a number of problems especially from application of derivatives and definite integrals. These are the favourite topics and definitely there will be questions from them. You can't afford to lose marks in calculus because it is one of the easiest topic.
Enjoy calculus.

Thursday 20 February 2014

Board exams are coming

Board exams are near. Pressure must have increased. You must be thinking how to handle so much pressure ? Boards -> JEE Main -> JEE advanced !!
Life must be going too difficult. I know how it feels. I have been through the same last year.
Let me help you to make it a bit easy.
Most probably, your first exam will be English (you must have got your date sheet by now). Prepare whole heartedly for it. Dedicate 3-4 full days for it. Keep your JEE preparation aside and start preparing English. There are many guide books available in the market and they are really really helpful especially if you are a dummy school student (Like me :P ). It's very important to get at least above 80 in English otherwise your percentage will go down significantly (Remember you have to be in the top 20 percentile of your board). Read the text book prescribed for your board thoroughly and follow a guide book. Ask for help from your friends who are not preparing for JEE. Request them to teach you English lessons.
Attempt the paper with planning and everything should be fine.
Around 50% load should be gone off from your head after English paper is over.
Next usually you will have Mathematics then Physics then Chemistry.
Here is where the trick comes.
You have a great chance to prepare NCERT thoroughly. Study NCERT in great detail. Solve the examples given in maths book. They might seem trivial but remember that if you don't have a practice of "writing" a solution, then you will be facing problem in your Board exams. So better sit with a pen and paper and write down the solutions to even the easy questions. There are certain topics that are not present in JEE advanced syllabus but they are in Board syllabus. Make sure you cover them. That will not only help you in Board exams, but also in JEE Main.
Do the same with Physics and Chemistry (especially). Prepare NCERT thoroughly and you will be done with class 12th syllabus of JEE Main and JEE advanced too (partly). In this way, you aren't wasting your precious JEE time. Instead, you are utilizing it smartly.
Make sure to cover all the proofs and derivations in Physics. They are important.
Make sure you have seen papers of last 3 years and solved them properly.
Make sure you have memorized all the tables and diagrams mentioned in NCERT for both Physics and Chemistry.
Lastly comes the optional subject (Computer/Physical education/Hindi/any other).
For Physical education, you don't really need to burn the midnight oil. Just learn the headings and write the final answer in your own words. You will surely get 90+ but make sure to dedicate around 2 days to the optional subject.
Getting a 90% in Boards is not only easy, but also it is required especially if you are in ICSE or CBSE Board.
For CBSE, the GodBook is NCERT. Don't search for unnecessary guides and all. Guides are required for English and optional subject. For Physics, Chemistry and Maths, you don't really need a guide. You JEE preparation experience is sufficient.
Whatever I have written in this post applies by and large to all the boards. Syllabus may vary slightly. Make sure to follow the syllabus strictly. You should not end up wasting time on something that is not really required.
All the best.
Work hard and make everyone proud of you.
Comments and suggestions are welcome.
A post on JEE Main will be coming soon

Monday 17 February 2014

Co-ordinate your geometry - co-ordinate geometry

Co-ordinate geometry has a huge weightage in JEE and it is considered to be the easiest topic in JEE maths.
First of all, a chapter wise analysis, then relevant books and then concluding remarks are mentioned in this post.

1.) Basics : Cartesian coordinates, distance between two points, section formulae, shift of origin etc. They form the backbone of Co-ordinate geometry. Make sure to learn all formulas by heart. Locus problems form another set of problems from the point of JEE. Master them


2.) Straight lines : Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, incentre and circumcentre of a triangle. These are the topics as mentioned in JEE syllabus. Understand the various forms of a line and learn to apply the best form in a particular scenario. Family of straight lines is most important from the point of view of JEE problems. Also make sure to learn how and when to apply the parametric form of a straight line.


3.) Circles : Equation of a circle in various forms, equations of tangent, normal and chord.

Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
It's the simplest chapter. Understand the standard equations. This chapter contains a number of formulas such as - length of tangent from a point, equation of chord of contact, equation of chord with a given midpoint, equation of common tangent, finding radical axis, radical centre, etc. The formulas derived here are general and apply to ellipse, parabola and hyperbola as well. So better learn them by heart. The parametric form of a circle is very important.

4.) Parabola : Most of the equations that are derived in Circles chapter will work here. The parametric form is really important in all chapters of conics. An interesting topic is the reflection property of parabola which you might like to learn for solving paragraph type questions in JEE. Note that paragraphs are common from the chapters of coordinate geometry so better be prepared to se something new on JEE day. You won't be given the same old beaten up problems.


5.) Ellipse : Much of same as Circles. Again the parametric form is important. Auxiliary circle helps a lot in solving the questions of this chapter. Locus problems are frequently asked from this chapter. Parametric form will help you in solving locus problems.


6.) Hyperbola : Much of same as Circles and ellipse. Simple but confusing. Conjugate hyperbola and asymptotes and their properties are important. Some people face problems in this chapter. Reason is that this chapter marks the end of coordinate geometry. So, usually people get bored till this time and tend to neglect it. But keep in mind that paper setters know all this. And they are ready to trap you. A good student cannot afford to miss any chapter.


Books : TMH is the best book if you are aiming for a good rank. If you are looking to try something challenging and want to convince yourself that you know coordinate geometry, then go for Arihant Coordinate Geometry by SK Goyal. It's a good book. It contains enough subjective and objective problems. Make sure you do all


Concluding Remarks : Make sure that you know the parametric form of each curve, equation of tangent of slope "m", equation of normal of slope "m", equation of tangent and normal at any point (x,y) or in terms of parameter. These are the most important things and most problems will be done if you do them.


Revision : Any review package might help. Make sure you revise the formulas from some reliable source. Best way is to write down all of them in a sheet of paper and revise regularly. You will learn them only when you apply them. So solve as many problems as you can. You will enjoy it. For revision you may try TMH (unsolved problems).


Finally : I request you all not to ask me "Is this book enough for JEE ?", "will I get under 1000 rank if I do this ?".

I really don't know the answer to such questions. Nothing is enough for JEE. You can solve all the material available but still, you might not get the expected marks because of poor examination temperament (about which I will write soon in my next post).

All the best.

Enjoy coordinate geometry