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.

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 \(\sum _{ r=0 }^{ n }{ { 3 }^{ r } } \) ^{8}C_{r = 4n
Solution.
We have,
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