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How to do 30% of AIEEE exam in 20 minutes (Equations) Objective Tips and Tricks explained by problems (Chapter - 2) (note: this may be debatable. We do not want to go into debate. But the tips and tricks are actually helpful, and in fact at least helped me getting rank 5 in AIEEE and 32 in IITJEE screening) Brought to you by Youmarks Preparations Prepared by Parag Arora copyrights © youmarks.com

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Introduction This website has been extensively made to reflect the enormous advances in the preparation for the engineering entrance examinations. While the basic principles are largely the same which you may be studying from past 2 years in your schools and other sources, the new innovative ways of solving the questions will be taught. As we all know that the new examination pattern for all the engineering entrance exams like IIT JEE, AIEEE, BITS, DCE etc. now are the objective exams and the approach you need for them is totally different from that what you learn from all the conventional sources. Also do remember that examiner this time wants the right answer from you out of the four choices given to you, how you reached the answer you are marking does not bother him at all. All what you need at this last moment is the speed and accuracy, which we will try and provide you through the lessons and the model test papers.

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copyrights © youmarks.com Equations Equations have two sides Left Hand Side (LHS) and Right Hand Side (RHS). Now you will have to start looking at the questions as if they are equations given to you. Procedure to use the trick Extract an equation from the given question Now remember that you can put the value of the variables in the given equations according to your convenience Put the value of few variables to get the value of other variables How to select these variables Zero: Zero has a beautiful property that it eliminates the entire term when it gets multiplied with it. Zero is the most commonly used number which can solve our purpose easily. Where ever you find yourself clueless with some equation, try and put few numbers equal to zero, to reduce the no. of terms from your equations from the question. Also zero helps you out in reducing the length of the question many times. (Remember whenever examiner wants you to restrict yourself with any of the number, he gives the condition in the exam say for example if in an equation examiner wants that x can not be zero then he will clearly mention in the question itself that x is not equal to zero )

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copyrights © youmarks.com Example 1: AIEEE 2003 Now see here no where examiner has restricted you with any of the condition. So you can directly put n = 0 in the determinant by which straight away you get the answer of the determinant to be equal to zero.

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copyrights © youmarks.com Example 2: AIEEE 2003 Now again see here no where examiner has restricted you with any of the condition. So you can directly put n = 0 in the expression by which straight away you can delete option (B) and (C) also since the answer is not independent of n as we can confirm by putting n = 1 we can say correct answer is (A).

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copyrights © youmarks.com Example 3: AIEEE 2003 Now again see here no where examiner has restricted you with any of the condition. So you can directly put n = 0 in the expression by which straight away you can delete option (A) and (D) now by putting n = 1 we can say correct answer is (C).

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copyrights © youmarks.com Example 4: AIEEE 2003

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copyrights © youmarks.com Example 5: AIEEE 2004 Now again see here no where examiner has restricted you with any of the condition. So you can directly put n = 0 in the expression that means constant term in 1+x which is again 1 by putting n =0 in all options directly we can say that correct option is (2)

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copyrights © youmarks.com Example 6: AIEEE 2004 (Similarly you can find infinite such examples from AIEEE 2004,05,06,07 and will hopefully find in 08)

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copyrights © youmarks.com a tip In these questions you have to add f(1) + f(2) + f(3)....+ f(n). Now for n =1 we get only one term that is f(1) and for n = 0 we get no term to add that means answer should be zero. So in these kind of answers put n=0 so either you will get an impossible answer putting n = 0 or will get answer to be zero that means you have added nothing. If you are not getting the answer putting n = 0 put n =1 and try to solve. Note Similar concept is applicable over the integration the only thing in integration is you cant expect answer to be zero by putting upper limit lesser than one as in the case of integration limits are reversible.

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copyrights © youmarks.com Example 7: AIEEE 2003 Now again see here no where examiner has restricted you with any of the condition. So you can directly put n = 0 to get answer 1 delete option (B) and put n = 1 to get f(1) = 7 that is option (D) is the answer. Now again it is not necessary to put the value to be zero, you will have to judge for the best available options. This thing you can learn while doing the tests.

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copyrights © youmarks.com Examples from tricks (Similarly you can find infinite such examples from AIEEE 2004,05,06,07 and will hopefully find in 08)

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Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:

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