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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.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 1

Ex 8.1 Class 11 Maths Question 2.
\({ \left( \frac { 2 }{ x } -\frac { x }{ 2 } \right) }^{ 5 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 2

Ex 8.1 Class 11 Maths Question 3.
\({ \left( 2x-3 \right) }^{ 6 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 3

Ex 8.1 Class 11 Maths Question 4.
\({ \left( \frac { x }{ 3 } +\frac { 1 }{ x } \right) }^{ 5 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 4

Ex 8.1 Class 11 Maths Question 5.
\({ \left( x+\frac { 1 }{ x } \right) }^{ 6 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 5

Using binomial theorem, evaluate each of the following
Ex 8.1 Class 11 Maths Question 6.
\({ \left( 96 \right) }^{ 3 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 6

Ex 8.1 Class 11 Maths Question 7.
\({ \left( 102 \right) }^{ 5 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 7

Ex 8.1 Class 11 Maths Question 8.
\({ \left( 101 \right) }^{ 4 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 8

Ex 8.1 Class 11 Maths Question 9.
\({ \left( 99 \right) }^{ 5 }\)
Solution.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 9

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
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 10

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

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
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 12

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 \({ 9 }^{ n+1 }-8n-9=64k\)
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 13

Ex 8.1 Class 11 Maths Question 14.
Prove that \(\sum _{ r=0 }^{ n }{ { 3 }^{ r } } \) 8Cr = 4n
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 14

We hope the NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1, drop a comment below and we will get back to you at the earliest.

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