[*x*] = [*x*/2] + [(*x* + 1)/2]where, [*x*] is the greatest integer less than or equal to *x*

Preparation for group discussion and personal interview is more unstructured than preparation for the written exam. Break it down into small parts: current affairs, biodata, speech practice, and work experience.

In a group discussion, do not take an extreme stand. Have an opinion, but also accept (reasonable) flaws, if any, in it, and be willing to listen to other people.

If the production of rice in India is *x*% of total rice production in the world, and if there is a *y*% increase in the production of rice in India, keeping the production of other countries constant, then the increase in the production of rice in the world is *xy*/100%.

Networking with your seniors who have got into good institutes is a very useful asset. Ask them about specific tips regarding the institutes that nobody else will be able to provide.

Your academic background is one of the key areas where interview questions can be asked. Review the key subjects in your area of graduation/specialization.

If two objects are moving around a circular track starting at the same point and in the opposite direction, and if they meet for the first time at the starting point after completing *m* and *n* rounds (*m* is not equal to *n*), then *m* and *n* are co-prime.

Be prepared with specific, realistic goals that you can discuss with the interview panel. Break your goals down into short-term, medium-term, and long-term.

It is perfectly okay in an interview to say “I don’t know” once or twice.

Volume of a cone remains unaltered even if we change the location of the vertex anywhere on the plane parallel to the base of the cone.

Don’t make your interview a stress interview. It is up to the panelist to decide how your performance was. Let them do their job. You do yours as best as you can.

Be especially careful not to introduce esoteric keywords in your biodata that you are not comfortable speaking about.

If the coordinates of the vertices of a parallelogram PQRS are P(*a*, *b*), Q(*c*, *d*), R(*e*, *f*) and S(*g*, *h*) then *a* + *e* = *c* + *g* and *b* + *f* = *d* + *h*.

Know each point and every word in your biodata by heart. Put in points that you are comfortable speaking about or expanding upon.

Remove stage fright by participating in group discussions with friends. Make your own group, and ask one person to be the moderator.

If *a*, *b*, *c*, ... be the roots of equation *f*(*x*) = 0, then

The equation whose roots are -*a*, -*b*, -*c*, ... is *f*(-*x*) = 0

The equation whose roots are 1/*a*, 1/*b*, 1/*c*, ... is *f*(1/*x*) = 0

The equation whose roots are *ka*, *kb*, *kc*, ... is *f*(*x*/*k*) = 0

The equation whose roots are (*a* - *k*), (*b* - *k*), (*c* - *k*), is *f*(*x* + *k*) = 0

Learn to lead interviews by speaking keywords that attract interviewers to ask you follow-up questions on. This can make the difference between a successful interview, and an unsuccessful one.

If *f*(*x*) is a polynomial, then *f*(*k*) is the remainder when *f*(*x*) is divided by (*x* - *k*).

Write down the answer to “Tell us something about yourself” in detail, practice saying it in front of a mirror without sounding memorized, and use voice modulation.

The product of any *n* consecutive integers is divisible by *n*!.