principle of counting. Many problems relating to puzzles that we come

across in our daily life are solved by using the knowledge of

Permutations and Combinations. The concept of Permutations and

Combinations was treated as a self contained topic in Mathematics

under the name of ''Vikalpa" by renowned mathematician 'Mahavira' in

9th century A.D. The credit of stating several important theorems and

results on the subject matter of Permutations and Combinations goes to

the renowned

scholar ''Bhaskaracharya".

This chapter is significant in algebra as well as Probability in view

of a number of applications in day to day life. For instance, choosing

five questions out of seven questions in a question paper, choosing

required items from the menu card in a hotel, selecting a cricket team

of eleven players from out of sixteen members etc.. are based on the

principle of Permutations and Combinations only. The theory of

Probability is an extension of this chapter. Delegates occupying the

seats in a round table meeting is concerned to circular permutations.

Students must be aware of these types of practical problems and their

solutions. Students are expected to solve all the problems of all the

exercises in this chapter for gaining good marks. In competitive

entrance examinations, this chapter along with Probability chapter has

its own importance.

"Binomial theorem" is proved by using the principle of mathematical

induction, which was studied in First Year Algebra unit. Binomial

theorems for positive integral index and rational index have a number

of applications.

Binomial coefficients have many properties with which students are

expected to be perfect. Students are also advised to repeatedly

practise all the solved problems and all exercise problems. This is an

important

chapter in marks point of view. The application of binomial theorem

will be taken up in theoretical distributions in the Probability

chapter.

"Partial Fractions" and "Measures of Dispersion" are such easy

chapters that students need not put any extra effort than the required

one. It is more than sufficient if they are thorough with the methods

involved in them.

Probability

As said earlier, Probability is based on the concept of Permutations

and Combinations. It deals with the phenomenon of chance or

randomness. This chapter is extensively studied in the form of

postulates, results, theorems

and illustrations. The theory of Probability is simply the science of logic,

quantitatively treated. This is a good scoring chapter, once studied

in a proper way. In the chapters Permutations and Combinations and

Probability students are exposed to challenging problems sometimes in

competitive

examinations.

Many problems of Science as well as daily life are concerned with a

numerical value associated with the outcome of an experiment. For

example, we would like to know the probability of 10 coins showing up

8 tails when at a time tossed. To study problems of this type, the

concept of random variable is introduced. Students are expected to

know the formulae for finding mean and variance of a random variable.

Similarly knowledge of

binomial theorem and binomial coefficients is necessary to tackle the

problems of probability distributions. Marks wise, this is an easy

chapter for students.

To conclude the analysis about Paper-A, it is reminded that chapters

like Complex numbers, De Moivre's theorem, Theory of equations,

Permutations and Combinations, Binomial Theorem and Probability

require attention and hard work for performing well in the

examinations. Good Luck!

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