## JEE Main: Binomial Theorem and Its Simple Applications

## FAQs on JEE Main Important Chapter - Binomial Theorem and Its Simple Applications

Q1. Describe the usage of the Binomials.

Ans: The binomial distribution model permits us to calculate the probability of noticing a definite number of "successes" when the procedure is repetitive for a specific amount of times such as in a set of patients and the outcome for a specified patient is either a victory or a disappointment.

Q2. Give your idea about the importance of the Binomials.

Ans: The binomial distribution is highly important as it has a huge range of applications. The only reason is that its heart is a binary situation: one with two likely results.

We present a binomial unintended variable as the number of 'successes' in ‘n’ known as ‘independent Bernoulli trials, each having the same probability of success ‘p’.

Q3. Can you elaborate on the binomial theorem in statistics?

Ans: The binomial theorem which is occasionally known as binomial expansion is the most common method which is used in statistics as a simple formula.

This method (formula) is applied to calculate the probabilities for binomial experiments for the events which have two choices such as heads or tails.

Q4. Let’s calculate the coefficient of y9 in the expansion of (1 + y) (1 + y^{2}) (1 + y^{3}) . . . . . . (1 + y^{100}).

Ans:

Here, y^{9} can be fashioned in 8 ways.

Such as y^{9}^{,} y^{1+8}, y^{2+7}, y^{3+6},y^{4+5}, y^{1+3+5}, y^{2+3+4}

∴ The coefficient of y^{9} = 1 + 1 + 1 + . . . . + 8 times = 8.

5. How binomial theorem formula help to score high in the JEE Main Exam?

The binomial theorem is a strategic asset for JEE Main success. Its formula facilitates efficient expansion of expressions like $((a + b)^n),$ aids in calculating coefficients, identifies patterns, and solves combinatorial problems. Essential for probability, statistics, and series manipulation, the binomial theorem accelerates problem-solving, making it a key factor in securing high scores by providing versatile solutions across diverse mathematical challenges in the JEE Main exam.