Learn Mathematics with Free Lessons & Tips

Attempt:

Attempt all the questions whether you know the answer or not.

Neat and clean:

Answer sheet should be neat and clean. Do not forget to cut the rough work done. Avoid overwriting.

Observant:

Always note the terms and digits from the question paper carefully.

Organised:

Question paper must be solved in serial order from 1 to 30. If you don`t know the solution for a particular question, leave the space for that.

Patience:

Never lose your patience during the exam. If you do not know the answer to any question, do not lose your patience. Move ahead and after completing rest of the questions, take a long breathe and think about the concepts involved in that particular question. This will definitely help you to recall some steps of that question.

Points to remember in the examination hall:

•Read the question paper with full concentration.

•First, attempt those questions which you are sure about.

•Mention the formula and put the values while solving your question as there is a criterion of step marking.

•Use pencil and scale to draw the figures. Never draw a figure with the use of a pen.

•If your writing is poor, then you can write leaving some space in between two words.

When things are arranged in a circle then number of permutations ( arrangements ) is calculated in the following way :

Since one of the objects is always fixed in its position so the total number of objects to be arranged gets reduced by 1.

So if total n objects are there then no of permutations will be 

(1) when clockwise and anticlockwise permutations are counted different = (n-1)!

(2) when clockwise and anticlockwise are not counted different = (n-1)!/2

Permutation means arrangement

Fundamental principles of counting

If a work can be done in m ways and the either can be done in n ways, then the no .of ways in which both the works can be done is m×n ways.

But if they are done I depend on each other that is doing of one does not affect the other, then it is m+n.

The no of ways in which n different things can be arranged is n! Which is equal to

n!=n ×(n-1)×.....×2×1.

The no. of ways in which r things out of n things can be arranged is

n^P^r = n!/(n-r)!.

If any particular object is repeated p, q.. times then the result is divided by p! q!... respectively to get the desired permutation.

To find maximum and minimum value of a given function.

Differentiate the function first and then find the values of x at which the function becomes zero these are the possible points of Maximum and minimum values of the function then apply any of the following test

(1) 1st derivative test: If at any of the above values of x dy/dX changes its sign from +ve to -ve then that is a point of local Maxima.

And if dy/dX changes sign from -ve to +ve that is a point of local minima.

(2) 2nd derivative test: Find the 2nd derivative and put the above values of x obtained if it comes -ve that is a point of local Maxima and if it comes +ve that's a point of local minima.

Note: there can be more than 1 point of local Maxima and Minima

Global Maximum and Minimum: put all the values of x obtained in the function and check which one is largest, that value correspond to Global Maxima and that vale is global maximum. Similarly check for Global minima.

Note:sometimes 2nd derivative test fails i.e it becomes zero that that point is called point of inflection. Then check with first derivative test.