NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem.

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 8
Chapter Name	Binomial Theorem
Exercise	Ex 8.1, Ex 8.2
Number of Questions Solved	26
Category	NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

NCERT Exercises

Chapter 8 Binomial Theorem Exercise – 8.1

Expand each of the expressions in Exercises 1 to 5.
Question 1.

Solution.

Question 2.

Solution.

Question 3.

Solution.

Question 4.

Solution.

Question 5.

Solution.

Using binomial theorem, evaluate each of the following
Question 6.

Solution.

Question 7.

Solution.

Question 8.

Solution.

Question 9.

Solution.

Question 10.
Using Binomial Theorem, indicate which number is larger or 1000.
Solution.
Splitting 1.1 and using binomial theorem to write the first few terms we have

Question 11.
Find . Hence, evaluate .
Solution.
By binomial theorem, we have

Question 12.
Find . Hence or otherwise evaluate .
Solution.
By using binomial theorem, we have

Question 13.
Show that is divisible by 64, whenever n is a positive integer.
Solution.
We have to prove that

Question 14.
Prove that ⁸C_{r = 4ⁿ
Solution.
We have,}

Chapter 8 Binomial Theorem Exercise – 8.2

Question 1.
Find the coefficient of x⁵ in (x + 3)⁸
Solution.
Suppose x⁵ occurs in the (r + 1)^th term of the expansion (x + 3)⁸

Question 2.
a⁵ b⁷in (a-2b)¹²
Solution.
Suppose a⁵ b⁷ occurs in the (r + 1)^th term of the expansion (a – 2b)¹².

Write the general term in the expansion of
Question 3.
(x² – y)⁶
Solution.

Question 4.
(x² – yx)¹², x ≠ 0
Solution.
We have given, (x² – yx)¹² = (x² + (- yx))¹², x ≠ 0

Question 5.
Find the 4th term in the expansion of (x – 2y)¹².
Solution.

Question 6.
Find the 13th term in the expansion of , x ≠ 0
Solution.

Find the middle terms in the expansions of
Question 7.

Solution.
As the exponent 7 is odd, so there will be two middle terms in the expansion

Question 8.

Solution.

Question 9.
In the expansion of (1 + a)^m+n, prove that coefficients of a^m and aⁿ are equal.
Solution.

Question 10.
The coefficients of the (r – 1)^th, r^th and (r + 1)^th terms in the expansion of (x + 1 )ⁿ are in the ratio 1: 3: 5. Find n and r.
Solution.

Question 11.
Prove that the coefficient of xⁿ in the expansion of (1 + x)²ⁿ is twice the coefficient of xⁿ in the expansion of (1 + x)^2n-1.
Solution.

Question 12.
Find a positive value of m for which the coefficient of x² in the expansion (1 + x)^m is 6.
Solution.

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