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The IIT Entrance Exam

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Re: The IIT Entrance Exam

#91

Post by mjfl »

tzs wrote: post #89
scarmig wrote: post #21

Earlier quoted context omitted.

First one's simple enough, but second one I couldn't figure out if there's a clever trick. Or are students expected to apply the quadratic formula and do a bunch of symbolic manipulation?

There's an interesting connection between the roots of quadratic equations and Fibonacci-like sequences that is applicable to this problem. Let r and s be the roots of x^2 - ax - b, and let c[n] = (r^n - s^n)/(r - s). Then c[n] satisfies the recursion c[n] = a c[n-1] + b c[n-2]. For instance, if a = b = 1, then that sequence is the Fibonacci sequence, and the quadratic is x^2 - x - 1. r is then the golden ratio, s is…

I think it's easier to think about it as if you are just multiplying the original equations by some power of alpha or beta i.e.

alpha^(n-2)(alpha^2 - 6alpha - 2) = 0 = alpha^n - 6 alpha^(n-1) - 2 alpha^(n-2)

Hard to see without latex typing...

Re: The IIT Entrance Exam

#92

Post by NTDF »

rurounijones wrote: post #24

Think of the lost potential of the people who may still be the cream of the crop but just outside the 2%. The logical part of me says that they should be building more of these academies (if they can without sacrificing quality).

As a person just outside the 2% (yes, I failed those entrance exams) and yet currently residing in Silicon Valley, I disagree. I would much rather preserve the sanctity of those few colleges.

I'd rather have other universities collaborate/compete with the IITs. Not very different from how CMU is competing with IVY league universities here.

Re: The IIT Entrance Exam

#93

Post by tzs »

mjfl wrote: post #91
tzs wrote: post #89

Earlier quoted context omitted.

There's an interesting connection between the roots of quadratic equations and Fibonacci-like sequences that is applicable to this problem. Let r and s be the roots of x^2 - ax - b, and let c[n] = (r^n - s^n)/(r - s). Then c[n] satisfies the recursion c[n] = a c[n-1] + b c[n-2]. For instance, if a = b = 1, then that sequence is the Fibonacci sequence, and the quadratic is x^2 - x - 1. r is then the golden ratio, s is…

I think it's easier to think about it as if you are just multiplying the original equations by some power of alpha or beta i.e. alpha^(n-2)(alpha^2 - 6 alpha - 2) = 0 = alpha^n - 6 alpha^(n-1) - 2 alpha^(n-2) Hard to see without latex typing...

> Hard to see without latex typing...

MathJax to the rescue:

\[\alpha^{n-2}(\alpha^2-6\alpha-2)=0=\alpha^{n}-6\alpha^{n-1}-2\alpha^{n-2}\]

To render with MathJax, use the bookmarklet available here: http://checkmyworking.com/misc/mathjax-bookmarklet/

Re: The IIT Entrance Exam

#94

Post by dipkakwani »

I was one of the 1.3 million JEE aspirants this year. But I didn't join coaching classes. I believe that we study for acquiring knowledge rather than creating strategies for cracking exams which involves cramming thousands of formulas and shortcuts.These coaching institutes provide the poorest of study materials and low quality education.I prefer to study from internet.Most of the students waste there 2 years in preparing for JEE. I don't know why government encourage coaching institutes by asking questions that we are not taught at schools.Moreover, many of the IIT grads prefer to teach in coaching institute rather than going in industry and research.

I am immensely interested in computer science. I studied it a fair bit throughout the two years. I made an image editor as my project. But this backfired me as I couldn't devote my time to JEE preparations.I couldn't crack JEE Advanced.

JEE arises in students a feeling of competitiveness which prevails in them even when they are in colleges. Do you still think that this trade of coaching institutes is fair and that students should participate in this rat race?

Re: The IIT Entrance Exam

#95

Post by Ashuu »

lake99 wrote: post #78
simula67 wrote: post #63

Earlier quoted context omitted.

>huge amount of human potential is being wasted in India. Just a counterpoint : IITs are state funded, i.e most of the student fees are paid for by the government. Once they complete their education, do they not have a duty to give back to the people ? Remember, brain drain is a serious problem for countries like India.

Though my own taxes help fund the IITs, and I never was hard-working enough to get through the JEE, I'm happy that we have the IITs setting at least some kind of an example for the rest of India. I am disappointed by the idiots filling teaching positions in most other colleges. > do they not have a duty to give back to the people ? I hate this attitude, not just in India, but anywhere in the world. Like Kennedy's "as…

About the brain drain problem, I think yes. They would have accomplished more if they stayed in India. Just have a look at Narayan Murthy, founder of Infosys. Just imagine if people like Sundar Pichai, Vic Gundotra etc stayed in India, they might have done something even bigger than what they had done at Google. Android or something similar would have been created in India or India would have a social network like Google Plus! Who knows!

Re: The IIT Entrance Exam

#96

Post by th3iedkid »

chetanahuja wrote: post #75
th3iedkid wrote: post #70

Earlier quoted context omitted.

Given today's scenario the quality of engineers is dipping.So does the gap and thus even a decently meritorious engineer looks much better than the rest of the crowd.An old study http://careers.learnhub.com/news/544-90-percent-graduates-an... shows how poor the rest of the colleges are.That said the socioeconomic gap keeps widening and thus opinions.Opinions are hard to break lest someone disprove.Vast majority of in…

I'm finding it hard to decipher the point you're trying to make other than the fact that you're dissatisfied with... uhh... things in India. No argument there. I am too. The discussion at hand was about the small set of people who perhaps have the capability to get into IIT's but for various reasons don't manage to get in the top 2% in that particular test. I asserted that such people end up in other decent colleges…

Sorry my frustration overrode clarity!! the gap across good quality colleges and others is getting bigger and bigger by the day .Unless something is done,these off-center-2% might as well get mixed up and lost.i wanted to mention the sociology-economic gap outside of IIT scheme of things.Its usually expensive if it isn't IIT and when it gets to that it creates all the more gap.Priorities change from educating oneself to undoing ones debts quickly and these very same priories can take one in a very different course.This will only widen the socioeconomic gap and lessen the opportunity for bright minds to come out naturally in times to come.
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