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.

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 \[^{n+k-1}C_{k-1}.\]

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

---

Concepts tested:

Answer:

Solution:

---

---

Common mistakes:

---

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

---

Concepts tested:

Answer:

Solution:

---

---

Common mistakes:

---

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

---

Concepts tested:

Answer:

Solution:

---

---

Common mistakes:

---

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

---

Concepts tested:

Answer:

Solution:

---

---

Common mistakes:

---

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