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### 10 Keys to Unlock Mains

• Do not pay emphasis on new topic. It is quite difficult to master a new topic in limited time. It is better to practice the areas that you are already familiar with.
• There appears to be part-marking in mains. Keep that in mind while writing your answer.
• It is more important to do a question completely rather than trying to do more half-done questions.
• In a solution if a mistake is made initially though the later part is correct, there are less chances that the examiner is going to like it.
• Put yourself under test conditions once a week to get accustomed. Note that too much of test taking does not help. Only a deep understanding can get you through mains and not blind test taking.
• If your start is not good, i.e. the first paper does not go well, do not worry. Others may find it difficult as well. Remember, "When the going gets tough, the tough get going".
• Do not spend too much time in one question. Do the easy ones first.
• You may not get extra sheet to write. Practice well to do a question in limited space.
• Be mentally prepared for any surprise. It is possible but not necessary that the paper would be based on last year's pattern.
• Do approximations in calculations keeping an eye on the error.
Some additional points should be referred from the earlier article on tips for screening.

### A man starts walking from the point P (-3, 4) ....

A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR}$ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1$ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$