Contents

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 ^{8}C_{r = 4n
Solution.
We have,
}

### Chapter 8 Binomial Theorem Exercise – 8.2

**Question 1.**

Find the coefficient of x^{5} in (x + 3)^{8}

**Solution.**

Suppose x^{5} occurs in the (r + 1)^{th} term of the expansion (x + 3)^{8}

**Question 2.**

a^{5 }b^{7}in (a-2b)^{12}

**Solution.**

Suppose a^{5 }b^{7} occurs in the (r + 1)^{th} term of the expansion (a – 2b)^{12}.

Write the general term in the expansion of

**Question 3.**

(x^{2 }– y)^{6}

**Solution.**

**Question 4.**

(x^{2 }– yx)^{12}, x ≠ 0

**Solution.**

We have given, (x^{2} – yx)^{12} = (x^{2} + (- 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 a^{n} 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 x^{n} in the expansion of (1 + x)^{2n} is twice the coefficient of x^{n} in the expansion of (1 + x)^{2n-1}.

**Solution.**

**Question 12.**

Find a positive value of m for which the coefficient of x^{2} in the expansion (1 + x)^{m} is 6.

**Solution.**

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