# JEE Multinomial Theorem

This page will teach you how to master JEE Multinomial Theorem. We highlight the main concepts, provide a list of examples with solutions, and include problems for you to try. Once you are confident, you can take the quiz to establish your mastery.

## JEE Conceptual Theory

*As per JEE syllabus, the main concepts under Multinomial Theorem are multinomial theorem and its expansion, number of terms in the expansion of multinomial theorem.*

**Multinomial theorem and its expansion:**

If \(n\) is a positive integer, then \((x_1+x_2+x_3+...+x_k)^n=\sum \frac{n!}{n_1!n_2!n_3!...n_k!} x_1^{n_1} x_2^{n_2} x_3^{n_3}...x_k^{n_k},\)

where \(n_1,n_2,n_3,...,n_k\) are all non-negative integers such that \(n_1+n_2+n_3+\cdots+n_k=n.\)Finding coefficients in the multinomial expansion

**Number of terms in the expansion of multinomial theorem:**

- Number of terms in the expansion of \((x_1+x_2+x_3+\cdots+x_k)^n\), which is equal to the number of non-negative integral solutions of \(n_1+n_2+n_3+...+n_k=n,\) which is \[^{n+k-1}C_{k-1}.\]

## JEE Mains Problems

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## JEE Advanced Problems

\[ \begin{array} { l l } A) \, & \quad \quad \quad \quad \quad & B) \, \\ C) \, & & D) \, \\ \end{array} \]

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Once you are confident of JEE Multinomial Theorem, move on to JEE Sequence and Series.

**Cite as:**JEE Multinomial Theorem.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/jee-multinomial-theorem/