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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