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

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1.

• Binomial Theorem Class 11 Ex 8.2

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 8
Chapter Name	Binomial Theorem
Exercise	Ex 8.1
Number of Questions Solved	14
Category	NCERT Solutions

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,}

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