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### 10 Mantras for IIT JEE 2006

1. Read the instructions given in the paper carefully. Nothing has officially been announced about the no. of questions that will be asked or about the difficulty level or about exact nature of negative marking or even about pattern of questions. Be mentally prepared for any surprises.
2. Do the easy questions first. Leave the difficult ones at first go. Reach the end of the question paper this way. If you still have time, try to do the more difficult questions that you had left in the first go.
3. Wild guessing should not be done. However, if at least 50% of the options have been eliminated, then intelligent guessing may be done. This decision needs to be fine tuned after looking at the penalty factor. (If some questions do not have negative marking then this rule is not applicable for them. Any questions not having negative marking should not be left unattempted.)
4. Reach the examination hall well in time. It may be a good idea to visit the place in advance, so that you do not have difficulty in locating it on the exam day in case you are unfamiliar with the location.
5. If the paper is very tough, don't feel nervous. Remember that it is relative performance that counts. Others may find it tough also.
6. Do not mark in hurry. This may spoil all the work you have done. Remember that this is the only thing that is examined.
7. Take care of your health. The most important thing in this respect in exam season is drinking water.
8. Do not study a new topic a few days before the exam. Strengthen the topics you are good at.
9. Do approximations in calculations keeping an eye on the error.
10. There is no need to write all steps in objective type tests. If you have the habit of showing all steps, then it is time to do away with it at least in objective type tests to save time. Also, there is no need to follow conventional methods to solve questions. Many ways like elimination of options, boundary conditions, variable substitution, dimensional analysis etc. may be employed.

### $f(x)=x^6+2x^4+x^3+2x+3 $$\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$$n=?$

Let $f(x)=x^6+2x^4+x^3+2x+3,x \in R$. Then the natural number n for which $\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$ is _ _ _ _ . Solution Since the limit has $\left[ {\frac{0}{0}} \right]$ form, L.H. Rule is applicable. Thus, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $\Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$