**Mathematics BINOMIAL THEOREM Practice Sample Question Papers and Problems on JEE Mains MCQ Level in Pdf format**

Subtopic

Binomial expansion Identifying terms independent of “x” Ratio of two terms Middle term of binomial expansion Binomial coefficients Sum of different combinations of binomial coefficients Application of binomial expansion Problems on multinomial expansion

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#### **Importance of JEE Maths Binomial Theorem**** ****Problems**

Mathematics subject is very interesting subject, even maximum students favorite subject is maths. But Mostely candidates are doing not well in Maths subject Board / Entrance Exam. because few maths chapters are numerical based theoretical based, and few IQ based thats why doing not well. For example Mathematics Matrices and Determinants **chapter,**** **After differential chapter reading, we want do all examples of differential chapter and NCERT, illustrations, practice paper, question paper, jee mains, practice problems, Sample papers, Model Test Paper, Solved Practice Sample Paper.

**JEE Mains Binomial Theorem Formulas**

- Binomial Theorem. …
- General Term in a expansion: …
- Combinations or groups formula: …
- Middle term in a expansion: …
- Coefficient of x
^{m}in (ax^{p}+ b / x^{q}) … - Independent Term of x in (ax
^{p}+ b / x^{q}) … - Greatest Coefficients:

**B.T.**

If n is a positive integer, then binomial theorem is

(x+y)^{n}=^{n}c_{0}.x^{n}+^{n}c_{1}x^{n-1}y +^{n}c_{2}x^{n-2}y^{2}+^{n}c_{3}.x^{n-3}y^{3}+ ……. +^{n}c_{r}x^{n-r}y^{r}+ …. +^{n}c_{n}.y^{n}**General Term in a binomial expansion:**

In the binomial expansion of (x+y)^{n}, general term is denoted by T_{r + 1}and it is

T_{r + 1}=^{n}c_{r}.x^{n – r}.y^{r}

**Combinations or groups formula:**

^{n}c_{r}= n!/[( n – r ) !].[r!]

**Middle term in a binomial expansion:**

In the binomial expansion of (x+y)^{n}, middle term is T_{( n/2 + 1)}if n is even, and T_{(n + 1)/2}and T_{( n + 3)/2}, if n is odd.**Binomial Coefficients in the binomial expansion (x+y)**^{n}

^{ n}C_{0}, ^{n}C_{1}, ^{n}C_{2}, ^{n}C_{3},….. ^{n}C_{r}… ^{n}C_{n} are called Binomial Coefficients.

**Binomial Coefficient of x**^{m}in (ax^{p}+ b / x^{q})

The value of r of the term which contains the coefficient of x^{m}is

(np – m )/( p + q)**Independent Term of x in (ax**^{p}+ b / x^{q})

The value of r of the term which does not contain x is

( np ) / (p + q)

**Greatest Binomial Coefficients:**

In the binomial expansion of (x + y)^{n}, the greatest binomial coefficient is

^{n}c_{(n+1)/2},^{n}c_{( n + 3 )/2}, when n is an odd integer, and^{n}c_{( }^{n}_{/2 + 1)}, when n is an even integer.

**Numerically Greatest term in the binomial expansion: (1 + x)**^{n}

In the binomial expansion of (1 + x)^{n}, the numerically greatest term is found by the following method:

If [( n + 1 ) | x | ] /_{[| x | + 1}] = K + f,

Where K is an integer and f is a positive proper fraction, then

( K + 1)^{th}term is the numerically greatest fraction.

And if [( n + 1 ) | x | ] /_{[| x | + 1}] = K,

Where K is an integer, then

K^{th}term and ( K + 1 )^{th}terms are the two numerically greatest terms.

**In the binomial expansion of (x+y)**^{n}:

**1. Sum of the binomial coefficients is 2**^{n}

^{n}c_{0}+^{n}c_{1}+^{n}c_{2}+ …………+^{n}c_{n}= 2^{n}

**2. Sum of the odd binomial coefficients is 2**^{n – 1}

c_{1}+ c_{3}+ c_{5}+ …………. = 2^{n – 1}

**3. Sum of the even binomial coefficients is 2**^{n – 1}

c_{0}+ c_{2}+ c_{4}+ …….. = 2^{n – 1}

**Number of terms in various expansions:**

No. of terms in the expansion of

1. ( x + y )^{n}is n + 1

2. ( x + y + z )^{ n}is^{[( n + 1 ) ( n + 2 )]}/_{2}

3. ( x + y + z + w)^{n}=^{[ ( n + 1)(n + 2 ) ( n + 3 )]}/_{ 1. 2.3}

**What are significant topics in maths for the JEE Mains and Importance of Maths Matrices and Determinants Chapter?**

If you are talking about jee mains and advanced, so each and every topic are important. So Cover all the topic of NCERT Mathematics Class 10, 11, 12 glowing. You should have to have six to seven years question paper of jee mains and advanced both students so that you will get to know about the question level and paper pattern.

*Even maths is very important in our life, because its used to complete many different tasks daily, for examples in the bank, hospital, shops, pharmacists engineers, nurse, stock market, investment, IQ development, use maths every days to perform their expert duty well. Maths makes our life orderly. Everyone require maths*

Maximum students doing not well in mathematics subject Board / Entrance Exam. Maximum chapters are numerical based theoretical based, and few IQ based thats why doing not well. For example limit** **chapter, After differential chapter reading, we want do all examples of differential chapter and NCERT, illustrations,