NCERT Solutions | Class 11 Maths Chapter 8

NCERT Solutions | Class 11 Maths Chapter 8 | Binomial Theorem 

CBSE Solutions | Maths Class 11

Check the below NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Pdf free download. NCERT Solutions Class 11 Maths  were prepared based on the latest exam pattern. We have Provided Binomial Theorem Class 11 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 11 Maths

NCERT Solutions Class 11 Maths

Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	11th
Subject:	Maths
Chapter:	8
Chapters Name:	Binomial Theorem
Medium:	English

Binomial Theorem | Class 11 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 11 Maths Chapter 8 Binomial Theorem to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1

Expand each of the expressions in Exercises 1 to 5.

Ex 8.1 Class 11 Maths Question 1.
\({ \left( 1-2x \right) }^{ 5 }\)
Solution.

Ex 8.1 Class 11 Maths Question 2.
\({ \left( \frac { 2 }{ x } -\frac { x }{ 2 } \right) }^{ 5 }\)

Solution.

Ex 8.1 Class 11 Maths Question 3.
\({ \left( 2x-3 \right) }^{ 6 }\)
Solution.

Ex 8.1 Class 11 Maths Question 4.
\({ \left( \frac { x }{ 3 } +\frac { 1 }{ x } \right) }^{ 5 }\)
Solution.

Ex 8.1 Class 11 Maths Question 5.
\({ \left( x+\frac { 1 }{ x } \right) }^{ 6 }\)
Solution.

Using binomial theorem, evaluate each of the following

Ex 8.1 Class 11 Maths Question 6.
\({ \left( 96 \right) }^{ 3 }\)
Solution.

Ex 8.1 Class 11 Maths Question 7.
\({ \left( 102 \right) }^{ 5 }\)
Solution.

Ex 8.1 Class 11 Maths Question 8.
\({ \left( 101 \right) }^{ 4 }\)
Solution.

Ex 8.1 Class 11 Maths Question 9.
\({ \left( 99 \right) }^{ 5 }\)
Solution.

Ex 8.1 Class 11 Maths Question 10.
Using Binomial Theorem, indicate which number is larger\({ \left( 1.1\right) }^{ 10000 }\) or 1000.
Solution.
Splitting 1.1 and using binomial theorem to write the first few terms we have

Ex 8.1 Class 11 Maths Question 11.
Find \({ \left( a+b \right) }^{ 4 }-{ \left( a-b \right) }^{ 4 }\). Hence, evaluate \({ \left( \sqrt { 3 } +\sqrt { 2 } \right) }^{ 4 }-{ \left( \sqrt { 3 } -\sqrt { 2 } \right) }^{ 4 }\).
Solution.
By binomial theorem, we have

Ex 8.1 Class 11 Maths Question 12.
Find \({ \left( x+1 \right) }^{ 6 }+{ \left( x-1 \right) }^{ 6 }\). Hence or otherwise evaluate \({ \left( \sqrt { 2 } +1 \right) }^{ 6 }+{ \left( \sqrt { 2 } -1 \right) }^{ 6 }\).
Solution.
By using binomial theorem, we have

Ex 8.1 Class 11 Maths Question 13.
Show that \({ 9 }^{ n+1 }-8n-9\) is divisible by 64, whenever n is a positive integer.
Solution.
We have to prove that \({ 9 }^{ n+1 }-8n-9=64k\)

Ex 8.1 Class 11 Maths Question 14.
Prove that \(\sum _{ r=0 }^{ n }{ { 3 }^{ r } } \) ⁸C_{r = 4ⁿ
Solution.
We have,}

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2

 Expand binomials using the binomial expansion method step-by-step.

Ex 8.2 Class 11 Maths 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

Ex 8.2 Class 11 Maths 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

Ex 8.2 Class 11 Maths Question 3.
(x² – y)⁶
Solution.

Ex 8.2 Class 11 Maths Question 4.
(x² – yx)¹², x ≠ 0
Solution.
We have given, (x² – yx)¹² = (x² + (- yx))¹², x ≠ 0

Ex 8.2 Class 11 Maths Question 5.
Find the 4th term in the expansion of (x – 2y)¹².
Solution.

Ex 8.2 Class 11 Maths Question 6.
Find the 13th term in the expansion of \({ \left( 9x-\frac { 1 }{ 3\sqrt { x } } \right) }^{ 18 }\), x ≠ 0
Solution.

Find the middle terms in the expansions of

Ex 8.2 Class 11 Maths Question 7.
\({ \left( 3-\frac { { x }^{ 3 } }{ 6 } \right) }^{ 7 }\)
Solution.
As the exponent 7 is odd, so there will be two middle terms in the expansion

Ex 8.2 Class 11 Maths Question 8.
\({ \left( \frac { x }{ 3 } +9y \right) }^{ 10 }\)
Solution.

Ex 8.2 Class 11 Maths Question 9.
In the expansion of (1 + a)^m+n, prove that coefficients of a^m and aⁿ are equal.
Solution.

Ex 8.2 Class 11 Maths 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.

Ex 8.2 Class 11 Maths 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.

Ex 8.2 Class 11 Maths Question 12.
Find a positive value of m for which the coefficient of x² in the expansion (1 + x)^m is 6.
Solution.

NCERT Class 11 Maths

Class 11 Maths Chapters | Maths Class 11 Chapter 8

Chapterwise NCERT Solutions for Class 11 Maths

NCERT Solutions For Class 11 Maths Chapter 1 Sets
NCERT Solutions For Class 11 Maths Chapter 2 Functions and relations
NCERT Solutions For Class 11 Maths Chapter 3 Trigonometric functions
NCERT Solutions For Class 11 Maths Chapter 4 Principle of mathematical induction
NCERT Solutions For Class 11 Maths Chapter 5 Quadratic equations and complex numbers
NCERT Solutions For Class 11 Maths Chapter 6 Linear Inequalities
NCERT Solutions For Class 11 Maths Chapter 7 Permutations and combinations
NCERT Solutions For Class 11 Maths Chapter 8 Binomial Theorem
NCERT Solutions For Class 11 Maths Chapter 9 Sequences and series
NCERT Solutions For Class 11 Maths Chapter 10 Straight lines
NCERT Solutions For Class 11 Maths Chapter 11 Conic sections
NCERT Solutions For Class 11 Maths Chapter 12 Introduction to three-dimensional geometry
NCERT Solutions For Class 11 Maths Chapter 13 Limits and derivatives
NCERT Solutions For Class 11 Maths Chapter 14 Mathematical Reasoning
NCERT Solutions For Class 11 Maths Chapter 15 Statistics
NCERT Solutions For Class 11 Maths Chapter 16 Probability

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