How to use the 40 days between JEE Main and Advanced, 2017

JEE Main is over now. Even the cribbing about the lengthy mathematics questions and spending excessive time on it without any concomitant fruitful result should be over by now. If you have guessed your marks in JEE Main fairly well and if it is greater than 100, it’s time to focus on the mother of all competition, i.e. the JEE Advanced. If your guess is below 100, you still have to do it because you never know what can be the cut-off and you may get lucky. If you have faced the problem of lengthy and time consuming mathematical problems, most probably all the aspirants faced the same. So don’t lose heart. You got 40 days and these must be used for revision, going through formulae, going through the past JEE Advanced questions once again, working through challenging & tricky concepts, and fixing the small gaps that you have in important chapters. I will mainly talk about mathematics. How can you IIT aspirants use these 40 days for most effective revision.

First of all you should categorize the topics of JEE Advanced based in your competence. Look at the list of topics in JEE Advanced. Against each topic, mark your competence; excellent, average, poor.

Topics of your highest expertise

For the topics where you have excellent competence, revise them completely once again. Look through all the concepts, work through tricky areas, and solve few questions from each topic. Since you have competence in the topic, this should not take much time. Devote about 15 days studying about 3 hrs a day (overall, not in a stretch). This is only for mathematics. These are the ones that would get you through JEE Advanced.

Topics of your average expertise

For topics where your performance seems to be average, list the sub-topics (topics under the topic) which give hard time. Usually, there are few sub-topics which create problems and shake your confidence in the whole chapter. For example, distribution could be a sub-topic under permutations and combinations which you may not be comfortable with. Similarly, functional equations could be a sub-topic under “relations and functions” which is giving you sleepless nights. Work on those topics. Go through at least 20-30 solved examples of each topic, look at the approach of the problem solving. Look at different approaches applied to different conditions.

For example, many functional equations can be solved using partial differentiation and substituting a constant value for one of the two variables, x and y. While partial differentiation may scare you, it is not very difficult to master. Few of the problems can be solved using the differentiation by first principle.

Similarly, you may have problem in geometric interpretation of complex numbers. Look at the types of questions asked in this area. The questions are not asking you to solve Coordinate geometry using complex numbers. What you need to do is to understand the equations representing ellipse, circle, angle bisectors etc. and learn the use of these equations in solving questions which mainly ask for maximum/minimum values, locus etc.

Remember that gaining competence on your average topics requires you to focus on the sub-topics which make you average. A focused effort of 5-6 hours on a sub-topic can make huge difference to your understanding. These are the areas which will make you attempt more questions.

Topics with little or no expertise

Your response to these topics depends on how much time you have. Spending too much time on your poor topics can eat into the precious time you have before JEE Advanced. I would suggest, if you are going to spend too much time on your poor topic, you can very well ignore it because JEE Advanced is not something you can sail through by last minute preparation. I assume that you do not have more than 10% of “important” syllabus under poor topic category.

Finally solve as many test papers and analyse

Try solving as many test papers as possible in the same JEE Advanced pattern. Try to take at least 2 full tests, i.e. 4 papers (each test has 2 papers of 3 Hrs duration each) in a week. Create the test environment at home and do the problems. Fix the time 3 Hrs and stop when the time is over. Check your answer and evaluate. Now the analysis part comes. In the next article, I will discuss how to analyse your performance in mock tests. The analysis is the most crucial part of your mock test exercises.

~ Pankaj Priyadarshi


How to prepare for English and Logical Reasoning for BITSAT


Weren’t Physics, Chemistry, and Mathematics enough difficult for BITSAT, then why did they had to add English and logical reasoning to it. Frankly speaking, it was not required but who wants frank opinion now a days.

So now that this is there in the BITSAT test paper, let’s see how you can prepare for it so that you do not lose out because of this silly language which gets too much importance in our country. To be fair, English language does have its own advantage in science and engineering but making it a criteria for admission in one of the top engineering colleges is taking things little far.

The first and foremost thing is not to be scared by it. Do not think that you are at a disadvantage compared to city cool dudes. The grammar part is equally good or bad. Even if there is slight advantage, you can overcome it in no time.

Second, do not spend much time on it. You can start preparing for English and logical reasoning just 3-4 months before the actual BITSAT test. 4 months is more than sufficient to prepare for English and Logical Reasoning part of BITSAT. Spend about an hour or two depending on your current level of English.

The best way to prepare is to solve previous year questions and improve your vocabulary. Most of the words used in the test will be known to you in a vague way but you should know the exact meaning of the word. For this, spend some time in reading the newspaper daily. Read the editorial everyday with underlining words whose meaning you are not clear with. Then look at the meaning in a dictionary. Connect the meaning in the given context or sentence. This whole exercise will take less than 30 minutes.

Pay special attention to phrases most commonly used. You should also know the uses of “who & whom”, “in and into”, “which versus that” etc. Understand the singular and plural uses especially of the nouns which have “s” in the end. There are many quirks in English language which can drive you crazy in the beginning, especially students who did not give much attention to the grammar part of the language. All these may sound difficult in the beginning but once you do few sentences and use them, they will be easy to handle.

As far as logical reasoning is concerned, it is mathematics in the most primitive form. Finding the pattern in pictures, spotting the missing number, Venn diagram and pictorial representation of sets, relationship questions etc. are common. The only way to gain expertise is by doing them. These are like puzzles which you used to solve when you were children. The standard is similar but the time is short which makes it difficult.

Finally, buy a good book on BITSAT. Arihant’s or Disha’s books are good enough. As far as preparing for PCM is concerned, you have anyway prepared for JEE mains and advanced and that is more than sufficient for BITSAT.

~ Pankaj Priyadarshi

JEE Main – Online versus Offline

Since JEE has started both online and offline version of the test, students have been facing the big question. Which should they choose? This is not an easy decision. The doubt lingers whether one gets selected for IITs and top schools or not. If the student clears, the common doubt is whether he or she should have scored a better rank in the other version. If one is not selected then there is more doubt on whether the other version would have been a better decision. Let’s look at both the systems and discuss pros and cons.

OFFLINE TEST: Advantages

Familiarity: All of us are familiar with this test pattern. You are given a question paper, you go through it, select what is easier and start solving them first and then try the moderately difficult ones and then at the end, the hardest one. We are fed on this diet since our childhood.

Look and feel: Despite the widespread use of laptop, computers, tablets, and pads, we still feel more comfortable with paper. Paper doesn’t strain your eyes. It is easier, connects with your mind faster, and conveys the meaning without any nuisance such as glare of screen, time ticker, and myriad other images and icons.

Comprehensive view of the paper: You get to see all the questions at once which gives you a way to plan your time accordingly. You can select the easiest ones to start with and gain confidence and composure. The psychological part is also very important in any competitive examination.

Play with pictures on the paper: If you are given a diagram to work with in a question, you can simply put additional information in the same diagram. In case of online tests, you have to redraw the diagram and then put the additional information. Hence offline tests save time.

ONLINE TEST: Disadvantages

The only disadvantage I see is availability of papers for rough work. You have to do all your calculations in the question paper itself with whatever space JEE organizers relented to leave for you. The other one is filling the circles for your answer. This is time consuming and worse is that you can’t even change your answer if you wrongly fill another circle.

Now let’s look at online test in details.

ONLINE TEST: Advantages

More time for preparation: 1 week is the time lag between offline and online test. There is absolutely no reason to give this extra week. Only JEE organizers can tell you the reason for this. But the reality is that online test takers get one extra week.

Learn from the mistakes of your offline peers: This may sound unimportant or even trivial but it does help to know what to avoid in the actual test. For example, in JEE Mains 2017, mathematics was lengthy. Students who started with mathematics and did not keep track of time, lost on marks. The lesson learnt was that you restrict your time for each subject.

Availability of rough papers: This is where online test scores big time over offline. Plenty of rough papers are available for calculations and diagram. You don’t have to struggle between the texts to do your calculation as in the case of offline test.

Option to change answer: If you want to change your answer, just go to the question on the screen and select other answer. This is huge advantage over offline

ONLINE TEST: Disadvantages

Unfamiliarity is a big disadvantage. We tend to use screens for entertainment purpose mostly, like for light reading, chatting, looking for information etc. But looking at a question on the screen and solving it on the paper is not very user friendly. You have to move your head up and down and oscillate between question and your calculations.

Though there are pros and cons of both the systems, students should choose what suits their habit or comfort. However, when in doubt, go for paper test.

~ Pankaj Priyadarshi

How to study permutations and combinations for JEE mains and advanced

One of the most important topics for competitive tests such as JEE mains & advance, BITSAT and many others is permutations and combinations (P&C). In almost all the years, questions have been asked from this chapter. Needless to say, the chapter requires focused and detailed study to be able to solve questions in tests. Here are some of the important things you can do to be a master of permutations and combinations.

Understand counting

The most basic thing in mathematics is simple rule of counting. This simple concept suddenly gets an altogether different meaning when you study P&C. Most of the students simply skip this because it looks simple. Don’t get deceived by its simplicity. The basic rules of counting are pretty easy but practice a lot of questions to have a sound understanding of the concepts. This is the foundation of P&C.

Make the sample space small

Many times, the questions use big numbers. Counting using big numbers is of course difficult unless you use the formulae of P&C. Unfortunately, using the formulae doesn’t get you confidence. While you can use formulae to solve a question, do not forget to check your answer by using smaller numbers. It is always beneficial to use small numbers and counting to verify your answer.

For example, when you have to find out how many regions multiple intersecting circles divide a space into. Start with 2 circles, increase it to 3, then 4, you will see a pattern. It is easy to predict the answer when you increase the number by one and also derive the answer in terms of number of circles.

Learn and memorize the formulae

Fortunately, P&C has very few formulae, unlike the formidable coordinate geometry where they never seem to end. However, students do not memorize even these formulae thinking that they can derive in tests. This is flawed reasoning though. Derivation eats into your limited time which can be used to solve few more questions in JEE. Avoid this thinking and memorize what nCr / nCr+1 is equal to and any such variants. There are few more which must be remembered. They will help you not only in solving P&C problems but also binomial series.

Work on different variants of the problem

Divide the chapter into various types. For example, principle of inclusion-exclusion could be taken as one type; derangement is taken as another type etc. For each type, solve as many questions as possible, not the same type of questions but vary it as you wish.

For example, when you solve distribution problems, you generally come across two major cases. “Null value allowed” or “null not allowed”. Think of different cases. What if a variable can take value between 3 and 10 only? What does this extra condition change in the problem?

For example, when you solve questions on arrangement of elements of two types where no two should be adjacent to each other, think of the other cases. What if no three elements of the same type are adjacent to each other? How many ways are possible for this?

For example, when you find factors of a given number, think of a case when you want to find only even factors or odd factors. What changes you need to bring to your solution?

When you solve derangement problems, what happens when two of the elements are exactly identical? Does interchanging their places can be counted as one if we do not change others’ places?

Check your work once more

This is extremely important. Many times, students tend to count a specific case multiple times. This problem is also known as double counting. Check your answer for double counting as it inflates you answers and of course the answer will be wrong.

Finally, mind the difference between the various cases. Even a small change in the condition changes the complete question and ways of solving. Distribution problem and arrangement problems are notorious for putting new conditions to make problems tricky.

Work in these areas and see the change in your performance at IITJEE entrance.


~ Pankaj Priyadarshi

Studying Mathematics – should you know the derivation of formula

While teaching for IIT entrance, I usually come across two types of students; One that wants to know the derivation behind every formula, and the other that just wants to use the formula to get through the exam and tests. Why to reinvent the wheel, they ask. So what is important, knowing the derivation as well or just knowing the formula with their uses in problem solving?

This is not to suggest that you should or should not learn the derivation but you should be judicious in spending time on derivation. Remember that mathematics requires lot and lot of practice and then little more practice in the limited time.

There are two types of formulas. The first type is that which has been derived by large body of complex work. We see them in simple form for our use. This gives us an impression that the formula must have been simple to derive. This may not be the case. For example, long ago, a great mathematician, Bertrand, decided to solve a question. This is famously known as Bertrand Ballot problem. There were two candidates in an election. Candidate Martin got m number of votes while candidate Nathan won n number of votes. Here m is greater than n. When the counting happens, what is the probability that Martin is always ahead of Nathan. This means at any given point, the vote count of Martin is always more than the vote count of Nathan. This was certainly not an easy task to arrive at the probability of the event. After lot of deliberations, calculations, and recursion, Bertrand arrived at the probability will be

This looks pretty simple but deriving it will take lot of time. Whether you should understand the derivation of this depends on your level of preparation. If you have completed your syllabus and have nothing better to do than go to movies, I would suggest you try to understand this derivation. However, if you have chapters left in mathematics, move on.

The second types of formulas are the ones that are derived to offer us a simple form so that we can remember it and use it for problem solving. They are not difficult to derive but the purpose of making them ready made is that they are often used in problem solving. Hence using it saves time. These are like plug and play in computer. Do we really need to know the derivation? The answer depends on whether learning the derivation adds to our understanding of the subject at hand. For example, derivation of equation of a pair of tangents drawn on a circle from a point outside the circle is a good way to understand how a line is defined. The formula is SS1 = T2. However, understanding the derivation in this case will help you in defining your approach to problem solving. For example, knowing the derivation of all the ready made equations in coordinate geometry will help you master the subject.

So use your discretion when deciding to invest time in learning the derivation. Time is precious. This is the only asset that you students have. A judicious use of time will take you ahead from your competitors.


~ Pankaj Priyadarshi

Infinity – the final frontier of mathematics

In mathematics, we often come across statements such as “x tends to infinity” or “x -> ∞”. Most of the students read it and proceed to solve questions as per their understanding and defined process, tips, and tricks. Have you ever thought about infinity as concept? A great mathematician Rene Descartes (of Descartes rule of roots of polynomials) said that infinity is beyond the understanding of humans because we are finite. Whatever it meant the idea was to show that the very concept of infinity touches upon the existence of God.

Infinity – venture into unknown

Mathematically, infinity refers to a very large number, larger than any number you can think of. As soon as you think of any number, it is always possible to add a number and make it larger. There is no end to it. Hence statements such as n = ∞, or x takes the value of infinity really have no meaning. The correct statement is “n tends to infinity” which means n is a large number larger than any other number.

Essentially infinity refers to idea of unlimited such as space, time etc. Remember the quote of Einstein, “Only two things are infinity; the universe and the human stupidity. And I am not sure of the former”. At least, we humans have something in infinite supply.

Infinity as a concept creates some interesting situation in mathematics.

2 concentric circles with different sizes have the same number of points on the circumference. How? Draw a line from the centre intersecting the two circles. For every point common to the line and the bigger circle, you have a corresponding point on the smaller circle. Hence shouldn’t the number of points be same. There is no way to refute this.

2 sets of unlimited objects have the same size. Let’s say a set A is set of natural numbers while set B is set of real numbers between 1 and 2. Since both the sets have infinite number of elements, they have the same size. Who can refute this too?

We know that 2 parallel lines never meet. Well, here comes infinity… the place where they meet, far away from the madding limits of mathematics. Similarly asymptotes meet the hyperbola at infinity. Looks like infinity must be a nice place for meeting people torn apart by the limits of human mind. Our Bollywood too has adopted the concept of humanity where the young couple suffocated by traditions and limiting values swear that they will meet in next birth. This is the translation of mathematical infinity into something simpler to understand.

There are many more baffling examples.

You can create infinity too at some situation

We have infinity in our grip is when we draw the slope of tangent to a curve. Just draw a vertical line touching a curve and you have created a tangent with slope of infinity.

In a quadratic equation, put the coefficient of x2 equal to 0 and you have just created an equation with one root as ∞. Off course the second root is –C/A. If you put both the coefficient of x2 and x equal to 0, you have created a quadratic equation whose both roots are ∞.

Infinity, by its very nature, is unknown. The only person who ever tried to unravel it was none other than the extraordinary mathematician Ramanujan on whose life Hollywood made Oscar-winning movie called “The man who knew infinity” based on a book by the same name by Robert Kanigel. We can only try to understand a miniscule part of the infinite.


~ Pankaj Priyadarshi

Which subject to attempt first in JEE Advanced/Mains

For an IIT aspirant, this is a difficult question to answer, even more difficult than the JEE Advanced one. I am not kidding… just ask any IIT aspirant. In this article, I will try to answer this question in little details. This is solely based on my own successful experience long back as well as experience of my students who cleared JEE advanced and now studying in various IITs.

While I have mentioned JEE Adavanced in this article, this can be very well applied to JEE mains test too.

Before we attempt to answer this question, first answer this. If you are given 1 hr for each subject, what would you choose? I am sure you would look at your strongest subject and choose it because you can score maximum in the given time thus increasing your chances of success.

However, the real test does not divide time between subjects. This hard task is given to you to divide your time as you wish. Indeed, man is condemned to be free. In the real test, you are given 3 hrs and about 75 questions (roughly 25 from each subject). In my view, if you are reasonably good or strong at Chemistry, start your answers with chemistry. There is good reason for this. In the beginning, you should not only solve questions right but also maintain the good attitude for the next 3 hrs. Chemistry will help you achieve this.

At the same time, restrict your time to chemistry. Make sure that you do not spend more than 40-45 minutes on it. It is extremely important to restrict the time because you will need the saved time in mathematics and physics. Any extra time spent on one subject will make you regret when you have to leave few easy questions because of lack of time later. But if you are not good at chemistry, avoid it in the beginning as starting with it will frustrate you in the very beginning spoiling your chances in mathematics and physics. Start with the strongest subject.

Once you are done with chemistry, you can choose the relatively stronger subject out of Mathematics and Physics. If you choose Mathematics, again restrict the time to 1.25 hrs. Do not cross this because you will have only an hour for Physics. Then go for Physics. If you choose physics, follow the same timeline.

The reason for spending maximum time on your strongest subject (out of mathematics and physics) is that you can deliver more marks per extra minute, i.e. your marginal productivity will be much higher (remember marginal word from your application of derivative problems…). For example, if I spend 15 minutes extra in my strong subject, I can possibly solve 3 questions right while spending the same amount of time in other subject may make me score just 2 questions right.

Finally, do remember that JEE Advanced has individual cut-off apart from overall cut-off. Hence you cannot ignore any part of the question paper. Moreover, this advice is purely from my experience, if you have been taking JEE Advanced mock tests and have other ways to approaching different subjects, please continue with the same if you manage to score well. At the end of the day, all we want is your success in JEE.


~ Pankaj Priyadarshi