**Tip #1: Remember that it’s a low scoring exam.**

It’s hard to believe it after going through more than 12 years of schooling. But it’s true. To get in the top 500 in the *entire country* you only need to score more than about 70% in the exam. To be in the top 5000 you only need more than about 40-50%. Contrast this with a school exam where to be in the top 5 in *your class* you need to score more than 90%.

What does this mean? This means you do not even need to understand the entire syllabus to qualify. In fact, you can completely ignore a significant portion of it and still perform very well. This means you can just find the topics you like and are good at and become *really* good at them. If you can solve 90% of the questions from 60% of the topics you will already score 54%, which is enough to qualify.

**Tip #2: Remember that JEE tests you on your understanding as opposed to memorization skills.**

JEE questions are not like the questions asked in school exams. But unfortunately, it’s hard to explain what exactly the difference is without going through lots of examples. Of course, one difference is that the questions are much more difficult. But there are various ways of making a question difficult. JEE uses one specific kind of difficult questions—questions that test your understanding of the subject matter.

This is crucial to understand during your JEE preparation so that you will know what kinds of things to focus on. I think one of the most succinct ways of explaining the difference is just quoting Richard Feynman:

The next Monday, when the fathers were all back at work, we kids were playing in a field. One kid says to me, “See that bird? What kind of bird is that?” I said, “I haven’t the slightest idea what kind of a bird it is.” He says, “It’s a brown-throated thrush. Your father doesn’t teach you anything!” But it was the opposite. He had already taught me: “See that bird?” he says. “It’s a Spencer’s warbler.” (I knew he didn’t know the real name.) “Well, in Italian, it’s a Chutto Lapittida. In Portuguese, it’s a Bom da Peida. In Chinese, it’s a Chung-long-tah, and in Japanese, it’s a Katano Tekeda. You can know the name of that bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird. You’ll only know about humans in different places, and what they call the bird. So let’s look at the bird and see what it’s doing—that’s what counts.” (I learned very early the difference between knowing the name of something and knowing something.)

So in short, school exams mostly test you on how well you know the names of things and JEE tests you on how well you know things. You should remember this during your preparation and focus exclusively on activities that enhance your *understanding*.

Now I realize that it’s hard to just read the paragraph above once and completely understand what I am talking about, specially after going through ten years of schooling. So how does one understand the meaning of understanding? By reading good books, solving challenging problems yourself, and interacting with good-quality mentors and tutors. And I will leave it at that for now. Hopefully future posts will be able to explain this more thoroughly.

**Tip #3: Do not get nervous during the exam.**

Many students who have done everything right still fail in the exam because they get too nervous. Some nervousness is unavoidable. But try to keep it to a minimum.

I know that asking someone to not get nervous is exactly the kind of thing that’s likely to make them even more nervous. So I’m sorry to bring it up right now. But let me compensate by offering two tips that will genuinely help with nervousness.

First, any skill is learned with practice. Same is true for the skill of not getting nervous. Put yourself in lots of stressful situations where normally one would get nervous and try to maintain calm instead. This will make you better at not getting nervous in several ways. For example, during the exam, it’s nice to be able to tell yourself something like this: “Come on, I gave an impromptu speech in front of 1,000 people once and won. I can handle IIT JEE.”

Sports offer an excellent environment for small stressful situations. Moreover, nervousness is a biological response which is guided by the hormonal composition of your body to a large extent and physical activities help regulate your hormones. So we highly recommend playing sports.

Second, meditation helps. Several highly successful people meditate on a regular basis and vouch for its effectiveness. Unfortunately, most meditation-related resources are full of junk information. But stay tuned, because we will soon write a post on meditation with recommendations for useful resources.

*Friday, May 15th, 2015. Written by admin. 1 comment.*

The fundamental lesson of time management is that if you feel you need to manage your time, then things have already gone wrong. If that’s true, you can still recover, but that will require you to get into damage control mode and this post is not about that. This post is about setting up the parameters of your life in such a way that you sail through it without feeling that you lack time.

How does one achieve that? The answer is that instead of trying to manage time, you should focus on managing attention, energy, and motivation.

**Attention management**

Attention determines the rate at which you will get work done in the same amount of time. A typical work hour in modern times is full of distractions. Your email, text, and social networking apps are constantly open trying to notify you of every single event as soon as possible. This creates a huge overhead and drastically compromises one’s productivity. An hour spent working in isolation with all electronic equipments on a do-not-disturb mode is several times more productive than otherwise. For more tips on how to cultivate similar “deep work habits” visit Cal Newport’s blog.

OK, so switching off electronic equipments is the obvious thing you can do to improve attention. What else? Improving attention is equivalent to eliminating distractions. So what other sources of distraction can we eliminate? We often get distracted if we are not certain about what we want to work on. If you sit at your work desk with the goal “get better at math” you will spend a lot of time deciding whether doing something will make you better at math or not. For example, say in order to get better at math, you sit down with a set of exercise problems in combinatorics where you encounter the notion of the Catalan number. You get curious and fire up your browser to check out the Wikipedia page on Catalan number. You quickly glance through many mathematical formulas and reach the History section on the page where you read Euler’s name, which reminds you of Project Euler and you get curious to know why this guy’s name keeps showing up whenever you read about math. Several clicks and an hour later you know everything about Euler but have hardly made any progress with your exercise problems. So even though you are now more likely to win the next Math Trivia contest, this hour should be called a distraction because it was not the aim you started with.

Productivity experts have developed several tools to fight these kinds of distractions. The central idea is to reserve a block of time and be very articulate about what you want to achieve in that block. For example, you could reserve a one-hour block with the precise aim of “solving as many problems as you can from this set of 20 exercise problems in combinatorics.” This is precise and makes it much easy to decide whether something contributed towards this goal or not. For example, if you open Wikipedia to fulfill some temporary curiosity, it satiates your curiosity and that’s all. It does not help you progress toward your goal of solving those 20 exercise problems.

What’s the ideal length of a block of time to reserve for focussed activities? It depends on you. Clearly, a 4-hour long block is usually not good. Focussed work is taxing and doing it for four hours at a stretch is close to impossible. The pomodoro technique posits that the ideal block is 25-minutes long. We suggest that you experiment with it for a while and figure out what works best for you.

Finally, one can also optimize attention by playing around with the time of the day when one is most productive. The human body operates in a rhythm that makes certain times of the day more productive than others. Some people are more productive early in the morning and some in the night. But for most people there is a specific block of about 2-3 hours per day when their productivity hits its peak. It’s important to figure out what that block is for you and exploit it to its fullest.

To summarize:

- Find a block of about 2-3 hours per day when you are most productive.
- During those 2-3 hours, switch off all your email and social networking apps.
- Make a list of precisely defined goals that you want to work towards in those hours and devote your full attention towards those goals.

**Motivation management**

It is hard to consistently force yourself to do things that you hate doing. At the same time, work is work and it’s unreasonable to assume that you can truly enjoy your work all the time. No matter how much fun your work is, there will be times when getting together with friends and making stupid jokes will be way more fun. So you can’t always enjoy your work and you shouldn’t always hate your work. The more motivated you feel about your work the more productive you are going to be. Thus it’s important to maximize motivation. How does one do that?

First, the obvious. You should pick something to work on that feels like fun at least sometimes. If you have never enjoyed problem solving in your life, do not pick a career based on math. If you hate writing and have never enjoyed reading literature, then no need to try to become a writer. So let’s assume that you have picked a career wisely. What else can you do to maximize motivation?

Social circle is the biggest determining factor in how motivated you will feel for working towards your goals. The primary source of motivation in humans—and, in fact, in all other species—is social reward points. Subconsciously, we all work towards being recognized as a respectable member of our own social circles. So you should engineer your social circle so that this fundamental driving force works towards helping you achieve your goals. Hang out with people who are working passionately on goals similar to yours. If you want to pick one thing to do right now, this is it. The impact of a smart, energetic, and productive social circle cannot be underestimated.

These two steps should get you to about 80% of the maximum motivation level you can achieve. You can perform further tweaks by gamifying things. Measure your progress, create fun little competitions, compete with yourself and with your friends, create records, break records, and so on.

To summarize:

- Pick a career that does not make you do many things you hate doing.
- Hang out with people working passionately towards goals similar to yours.
- Gamify!

**Energy management**

This is usually not an issue with the younger crowd, but it is important that your body feels energetic a reasonable amount of time. If you feel sleepy all the time then you should fix that. How? The three most important areas to focus on are diet, sleep, and exercise.

Everyone should exercise, no matter what their age. At the minimum, pick up a sport and play it regularly. Sports are fun and will not only keep you healthy, but also help you grow as a person. Sports teach you how to perform under pressure: a skill that comes in handy at every important occasion in life. If you cannot play a sport, then make arrangements to be physically active at home. Buy a pair of dumb bells and lift them every alternate day. Or buy a resistance band and do some resistance training. If you do not want to buy anything, try body-weight fitness. There are many online communities where people working on their fitness get together and share tips and tricks. One example is the body-weight fitness subreddit. If you do not like any of the suggestions above, just go out and jog. Being active at least 20 minutes per day is *much* better than not being active at all.

Next thing is sleep. Going to bed at a regular time every day has immense advantages. At a young age, this may not be a big issue but older you get, the more benefits you will see from fixing your sleeping schedule. But in any case if you do feel lethargic most of the day, then an irregular sleeping schedule could be causing it.

Finally, eat healthy. Eat nutritious food and avoid junk food. We cannot explain in this one small post what constitutes healthy food. But the fundamental principle is that healthy food gives you all essential nutrients in the proportion that’s best suited for the body. Buying cooked food outside hardly ever achieves this. Restaurants and fast-food chains are trying to maximize their profits, which means they siphon millions of dollars of money into researching the food that’s most likely to get you addicted, not the food that’s most likely to keep you healthy. In short, staying off of pizzas, lays, and samosas is a good thing. Eating home-cooked food rich in a variety of nutrients is a good thing.

To summarize:

- Be physically active.
- Try to go to sleep at the same time every day.
- Eat nutritious food. Avoid junk food.

If you do the things described in this article, you will not feel the need to “manage time”. And that’s how time is managed.

*Sunday, May 10th, 2015. Written by admin. No comments.*

Multiple-choice questions are amenable to a new set of tools that are not available otherwise. To solve a multiple-choice question, you just need to figure out which option is correct. You do not necessarily need to solve the question itself.

As JEE 2015 approaches fast, let me demonstrate this method by showing you how to solve a question from JEE 2012 without really solving it.

Q. Perpendiculars are drawn from points on the line \(\frac{x+2}{2} = \frac{y+1}{-1} = \frac{z}{3}\) to the plane \(x+y+z=3\). The feet of the perpendiculars lie on the line:

- \(\frac{x}{5} = \frac{y-1}{8} = \frac{z-2}{-13}\)
- \(\frac{x}{2} = \frac{y-1}{3} = \frac{z-2}{-5}\)
- \(\frac{x}{4} = \frac{y-1}{3} = \frac{z-2}{-7}\)
- \(\frac{x}{2} = \frac{y-1}{-7} = \frac{z-2}{5}\)

Before starting to solve the question, look at the four options. All of them are of the form \(\frac{x}{a} = \frac{y-1}{b} = \frac{z-2}{c}\). What does this mean?

To specify a line in three (or higher) dimensions, you need to specify two things: its slope and one point that it passes through. In the representation above, the numerators are used to specify the latter and the denominators are used to specify the former. In particular, note that the point \((0, 1, 2)\) lies on the line in all four options above, since if we put \(x = 0, y = 1, z = 2\) in the four equations above, we get \(0 = 0 = 0\) in all four of them. This means the question is not really asking you to find the line defined by the feet of the perpendiculars. It’s asking you to only find the *slope* of the line defined by the feet of the perpendiculars. So if you solve the entire question, you will end up doing extra work—work that you were not even asked to do!

So how do you calculate the slope of the line? Before starting to frantically scribble formulas on a piece of paper, let’s do a few preliminary tests. What properties should the slope of the line we are looking for satisfy? We are looking for the line that is defined by the feet of the perpendiculars drawn from a given line to a given plane. The foot is where the perpendicular intersects the plane. This means the foot always lies on the given plane and that means the line we are looking for must also lie in the given plane. What property does the slope of a line lying in the plane satisfy? Yes, the slope must be perpendicular to any line that’s perpendicular to the plane.

For convenience, let’s call the given line \(L\), the given plane \(P\), and the line we need to find \(L’\). Lines perpendicular to \(P\) are all parallel to the vector \((1, 1, 1)\). That means the slope of \(L’\) should be such that \(L’\) is perpendicular to the vector \((1, 1, 1)\). So if \(L’\) is \(\frac{x}{a} = \frac{y-1}{b} = \frac{z-2}{c}\), then the inner product between \((1, 1, 1)\) and \((a, b, c)\) must be 0, that is, $a+b+c = 0$. So that’s a good test. We can now immediately eliminate all the options that do not satisfy this property. Unfortunately, there is no such option—all of them satisfy the property. The examiner was clever!

Another nice thing to test is whether \(L\) intersects \(P\) or not. If it doesn’t, then \(L\) is parallel to \(P\) and that will imply that \(L’\) must have the same slope as \(L\). That will immediately give us the answer we are looking for. If \(L\) is not parallel to \(P\), however, then it must intersect \(P\). Let’s say the intersection point is \(p\). Where is the foot of the perpendicular drawn from \(p\)? Yes, the foot is also at \(p\). That means \(p\) must lie on \(L’\) as well. Knowing a point that lies on \(L’\) is only going to help us find \(L’\). So it seems this is going to be a useful test.

The easiest way to check whether \(L\) intersects \(P\) or not is to see if it’s parallel to \(P\) or not. It is parallel to \(P\) only if the inner product of \((2, -1, 3)\) with \((1, 1, 1)\) is 0. But the inner product is 4, which means \(L\) intersects \(P\). Good, that means if we find the intersection point \(p\), we will get a point that lies on \(L’\). But there is another issue. We already know a point that lies on \(L’\), namely, the point \((0, 1, 2)\). We know this just because all four options pass through \((0, 1, 2)\). So what if this is the point \(p\)? In that case, we will not gain any new information. So it’s worthwile to check if \(p\) is the point \((0, 1, 2)\) or not. The easiest way to check that is to simply substitute \((0, 1, 2)\) into the equation of \(L\) and see if it satisfies. It does not. So \((0, 1, 2)\) does not lie on \(L\) and hence cannot be \(p\). This is great news! This means all we need to do is find \(p\), because that will give us not one, but *two* points that lie on \(L’\)! And two points uniquely determine a line!

So let’s find \(p\). This is the only time we will do some real calculations. Everything so far was just either trivial substitutions or spatial reasoning coupled with good imagination. To find where \(L\) intersects \(P\), we write \(L\) in a parametric form. That is, we write \(\frac{x+2}{2} = \frac{y+1}{-1} = \frac{z}{3} = t\) and conclude that any point lying on \(L\) must be of the form \((2t-2, -t-1, 3t)\) for some value of \(t\). Now substituting this into the equation for \(P\), we find that \(t = 1.5\) and therefore \(p=(1, -2.5, 4.5)\). Now the other point that lies on \(L’\) is \((0,1,2)\) and therefore the slope of \(L’\) is \((1, -3.5, 2.5)\), or renormalizing, we get a slope of \((2, -7, 5)\). And now we are done. Correct answer is option 4.

To summarize, here is what we did. Let \(L\) and \(P\) be the line and the plane given in the question, and \(L’\) be the line we need to find.

- Realize that \(L’\) must pass through \((0,1,2)\). Why? Because all four options pass through \((0,1,2)\). Note that this is something you would have missed if you had started solving the question without looking at the options.
- Notice that \(L\) is not parallel to \(P\) and thus it must intersect \(P\). Let’s call the intersection \(p\).
- Notice that \((0,1,2)\) does not lie on \(L\). Thus if we find \(p\), we will get
*two*points that pass through \(L’\) thus uniquely determining \(L’\). - Find \(p\), subtract it from \((0,1,2)\) to calculate the slope of \(L’\). Pick option 4 because that has the correct slope.

I know what you are thinking at this point. “Where do I find more tips and tricks like this one?” To the best of our knowledge, we do not really know of a resource that demonstrates these tricks catered towards the IIT-JEE. However, the book titled Street-Fighting Mathematics written by the MIT professor Sanjoy Mahajan does attempt to teach the art of “educated guessing and opportunistic problem solving” and we highly recommend it. The book is also accompanied by an online course. More information can be found here.

*Friday, May 8th, 2015. Written by admin. No comments.*

Two kinds of resources are going to be useful to an ambitious high school student trying to engineer a bright future for himself/herself: resources that provide advice and resources that provide knowledge.

**Advice resources:**

A recurring pattern that has emerged in career-related advice is that passion is overrated. People generally tend to feel passionate about things that they turn out to be good at. So the idea that one should find a field they are passionate about and then become good at it is kind of backward. Becoming good at something and becoming passionate about it happen together. The best way to pick a field is to use *external inputs* to judge how likely it is that you are going to enjoy the field in future and once you’ve found something good enough, become really good at it. This will automatically make you passionate about the field as well. Anyway, the reason I mention this is to point you to the excellent blog maintained by Cal Newport at. He is a big proponent of the passion-is-overrated theory and offers generally good advice on his website. Another similar blog is the one maintained by Scott Young.

**Knowledge resources:**

This of course depends on the kind of knowledge you want to acquire. But assuming you are a high-school student trying to become exceptionally good at Physics, Chemistry, and Mathematics, I would point you to the Physics Stackexchange, the Chemistry Stackexchange, and the Mathematics Stackexchange respectively.

The fundamental law of learning is that you learn ten times more by solving problems than by passively reading through a textbook. The Stackexchange communities make problem solving way more fun that it already was. On each website linked above, people from all over the world ask and answer questions. The website has set up a system of upvotes and badges on top of it that makes it too much fun. If you come up with an elegant solution to a question someone asked, not only will you gain satisfaction and knowledge, but you will also get more points! In short, the website has gamified the problem solving process and we highly recommend spending time there.

*Monday, April 27th, 2015. Written by admin. No comments.*

Here are some data related to JEE (Advanced) 2013 and some inferences that can be valuable for IIT aspirants. Some facts, like JEE (Advanced) is an easy examination and can be conquered easily with the right strategy, are clearly visible in these data. Common perception, like it is a very difficult examination, is primarily because majority of the students prepare very hard with a wrong strategy and fail to perform as per their potential. How else can you explain the fact that the marks scored by students who appeared in JEE (Advanced) 2013 varied between 332 and -70 out of maximum of 360? Remember that they all are quite brilliant students and have qualified through JEE (Mains). Look at the following data.

— Data:

The highest overall score for JEE 2013 has been 332 out of 360. This is 92.2% and is considered to be quite a slide from last year’s 96%.

Inference:

The questions asked in JEE can be answered within the given time. Students are able to score more than 90% here too.

— Data:

Only 23 students managed over 300 while 326 students scored over 250.

Inference:

70% of 360 (full marks) = 252. Since only 326 students could score above 250, a student scoring just 70% gets a rank in the top 326. It is so easy.

— Data:

The lowest mark scored this year is minus 70.

Inference:

If you are serious about JEE, don’t get amazed by the number of students taking the examination. Minus 70 and similar marks have been scored by those students who have qualified for JEE-Advanced on the basis of their performance in JEE – Mains. They are good students. Only wrong strategy can lead to such a disaster. Being you and having a right strategy is more important than anything else.

— Data:

The maximum questions unanswered were from mathematics.

Inference:

Yes, you don’t have to answer all the questions. You can leave quite a good number of questions unanswered. But, what is the fun in preparing so hard and leaving the questions unanswered? So much of time and effort goes wasted. Can we identify in advance, the time and efforts that are likely to go wasted and use them smartly on something more productive? Yes, it can be done.

— Data:

About 30-45% students allotted seats at the older IITs were successful on their second attempt.

Inference:

Majority of the seats are grabbed by students taking the first attempt. But 30-45% is not a discouraging figure for those taking the second attempt. They need to understand the challenges they are likely to face and be prepared for that. Remaining motivated for another year, studying the topics that they have studied so many times in the first attempt with same level of enthusiasm and handling distractions are some of the common challenges.

The data used here has been taken from an article published in Times of India. The article can be read here.

*Sunday, October 6th, 2013. Written by admin. No comments.*

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