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Edited By Ravindra Pindel | Updated on Jul 13, 2022 03:42 PM IST

In the previous exercise, you have already learned about the binomial expansion for positive integer and pascal triangle. In the NCERT solutions for Class 11 Maths chapter 8 exercise 8.2, you will learn about finding the general and middle terms of the binomial expansion. If you have understood the previous exercise of this chapter, you won't find any difficulty the get Class 11 Maths chapter 8 exercise 8.2. This exercise is very important for probability and statistics.

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You must try to solve all the NCERT book Class 11 Maths chapter 8 exercise 8.2 problems by yourself. If you have any doubt about this exercise, Class 11 Maths chapter 8 exercise 8.2 solutions are here to help you. These solutions are designed in a step-by-step manner so you can understand them very easily. Here you will get NCERT Solutions from Classes 6 to 12 for Science and Maths.

**Also, see**

in

Answer:

As we know that the term in the binomial expansion of is given by

Now let's assume happens in the term of the binomial expansion of

So,

On comparing the indices of x we get,

Hence the coefficient of the in is

Question:2 Find the coefficient of in

Answer:

As we know that the term in the binomial expansion of is given by

Now let's assume happens in the term of the binomial expansion of

So,

On comparing the indices of x we get,

Hence the coefficient of the in is

Question:3 Write the general term in the expansion of

Answer:

As we know that the general term in the binomial expansion of is given by

So the general term of the expansion of :

.

Question:4 Write the general term in the expansion of

Answer:

As we know that the general term in the binomial expansion of is given by

So the general term of the expansion of is

.

Question:5 Find the 4^{th} term in the expansion of .

Answer:

As we know that the general term in the binomial expansion of is given by

So the term of the expansion of is

.

Question:6 Find the 13^{th} term in the expansion of

Answer:

As we know that the general term in the binomial expansion of is given by

So the term of the expansion of is

Question:7 Find the middle terms in the expansion of

Answer:

As we know that the middle terms in the expansion of when n is odd are,

Hence the middle term of the expansion are

Which are

Now,

As we know that the general term in the binomial expansion of is given by

So the term of the expansion of is

And the Term of the expansion of is,

Hence the middle terms of the expansion of given expression are

Question:8 Find the middle terms in the expansion of

Answer:

As we know that the middle term in the expansion of when n is even is,

,

Hence the middle term of the expansion is,

Which is

Now,

As we know that the general term in the binomial expansion of is given by

So the term of the expansion of is

Hence the middle term of the expansion of is nbsp; .

Question:9 In the expansion of , prove that coefficients of and are equal

Answer:

As we know that the general term in the binomial expansion of is given by

So, the general term in the binomial expansion of is given by

Now, as we can see will come when and will come when

So,

Coefficient of :

CoeficientCoefficient of :

As we can see .

Hence it is proved that the coefficients of and are equal.

Answer:

As we know that the general term in the binomial expansion of is given by

So,

Term in the expansion of :

Term in the expansion of :

Term in the expansion of :

Now, As given in the question,

From here, we get ,

Which can be written as

From these equations we get,

Question:11 Prove that the coefficient of in the expansion of is twice the coefficient of in the expansion of .

Answer:

As we know that the general term in the binomial expansion of is given by

So, general term in the binomial expansion of is,

will come when ,

So, Coefficient of in the binomial expansion of is,

Now,

the general term in the binomial expansion of is,

Here also will come when ,

So, Coefficient of in the binomial expansion of is,

Now, As we can see

Hence, the coefficient of in the expansion of is twice the coefficient of in the expansion of .

Question:12 Find a positive value of *m* for which the coefficient of in the expansion is 6.

Answer:

As we know that the general term in the binomial expansion of is given by

So, the general term in the binomial expansion of is

will come when . So,

The coeficient of in the binomial expansion of = 6

Hence the positive value of *m* for which the coefficient of in the expansion is 6, is 4.

Class 11 Maths chapter 8 exercise 8.2 consists of questions related to finding the general term and middle term of the binomial expansion. There are some theorems and important points like the general formula for the general terms of binomial expansion, middle term when the number of terms is even, middle term when the number of terms is odd, etc. There are five solved examples given before the Class 11 Maths chapter 8 exercise 8.2 which you try to solve.

**Also Read| **Binomial Theorem Class 11 Notes

**Benefits of NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.2:-**

- Students are advised to solve more problems on their own, it helps them to understand the concept clearly.
- Class 11 Maths chapter 8 exercise 8.2 solutions are prepared by subject matter experts who have experience in this field, so you can reply to them.
- Class 11 Maths chapter 8 exercise 8.2 are prepared on the basis of CBSE guideline so it will help you to preppe for the CBSE final exam also.

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1. In the expansion of (a+b)^5 which term is the middle term ?

The 3rd and fourth terms of this expansion are the middle terms of this expansion.

2. The number of terms in the expansion of (a+b)^5 ?

The number of terms in the expansion = 5+1=6

3. What is the weightage of the binomial theorem in the CBSE Class 11 Maths ?

The weightage of the Algebra part in the CBSE Class 11 Maths is 30 marks. The chapter-wise weightage is not provided by CBSE.

4. Are these useful for revision before the CBSE exam ?

Yes, NCERT solutions are useful for quick revision before the CBSE exam.

5. In the expansion of (a+b)^6 which term is the middle term ?

Here the value of n is 6 so the number of terms will be 7 and the middle term would be fourth.

6. Do I need to buy CBSE class 11 solution book ?

No, you don't need to buy any solutions book for Class 11 Maths. You can find all the NCERT solutions for Class 11 online.

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