# NCERT solutions for Class 11 Mathematics chapter 8 - Binomial Theorem [Latest edition]

## Solutions for Chapter 8: Binomial Theorem

Below listed, you can find solutions for Chapter 8 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

Exercise 8.1Exercise 8.2Miscellaneous Exercise
Exercise 8.1 [Pages 166 - 167]

### NCERT solutions for Class 11 Mathematics Chapter 8 Binomial Theorem Exercise 8.1 [Pages 166 - 167]

Exercise 8.1 | Q 1 | Page 166

Expand the expression (1– 2x)5

Exercise 8.1 | Q 1 | Page 166

Expand the expression (1– 2x)5

Exercise 8.1 | Q 2 | Page 166

Expand the expression (2/x - x/2)^5

Exercise 8.1 | Q 3 | Page 166

Expand the expression (2x – 3)6

Exercise 8.1 | Q 4 | Page 167

Expand the expression (x/3 + 1/x)^5

Exercise 8.1 | Q 5 | Page 167

Expand (x + 1/x)^6

Exercise 8.1 | Q 6 | Page 167

Using Binomial Theorem, evaluate (96)3

Exercise 8.1 | Q 7 | Page 167

Using Binomial Theorem, evaluate (102)5

Exercise 8.1 | Q 8 | Page 167

Using Binomial Theorem, evaluate (101)4

Exercise 8.1 | Q 9 | Page 167

Using Binomial Theorem, evaluate (99)5

Exercise 8.1 | Q 10 | Page 167

Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

Exercise 8.1 | Q 11 | Page 167

Find (a + b)4 – (a – b)4. Hence, evaluate (sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4

Exercise 8.1 | Q 11 | Page 167

Find (a + b)4 – (a – b)4. Hence, evaluate (sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4

Exercise 8.1 | Q 12 | Page 167

Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate (sqrt2 + 1)^6 + (sqrt2 -1)^6

Exercise 8.1 | Q 13 | Page 167

Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.

Exercise 8.1 | Q 14 | Page 167

Prove that sum_(r-0)^n 3^r  ""^nC_r = 4^n

Exercise 8.2 [Page 171]

### NCERT solutions for Class 11 Mathematics Chapter 8 Binomial Theorem Exercise 8.2 [Page 171]

Exercise 8.2 | Q 1 | Page 171

Find the coefficient of x5 in (x + 3)8

Exercise 8.2 | Q 2 | Page 171

Find the coefficient of a5b7 in (a – 2b)12

Exercise 8.2 | Q 3 | Page 171

Write the general term in the expansion of (x2 – y)6

Exercise 8.2 | Q 4 | Page 171

Write the general term in the expansion of (x2 – yx)12x ≠ 0

Exercise 8.2 | Q 5 | Page 171

Find the 4th term in the expansion of (x – 2y)12 .

Exercise 8.2 | Q 6 | Page 171

Find the 13th term in the expansion of (9x - 1/(3sqrtx))^18 , x != 0

Exercise 8.2 | Q 7 | Page 171

Find the middle terms in the expansions of  (3 - x^3/6)^7

Exercise 8.2 | Q 8 | Page 171

Find the middle terms in the expansions of (x/3 + 9y)^10

Exercise 8.2 | Q 9 | Page 171

In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.

Exercise 8.2 | Q 10 | Page 171

The coefficients of the (r – 1)thrth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r.

Exercise 8.2 | Q 11 | Page 171

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 .

Exercise 8.2 | Q 12 | Page 171

Find a positive value of m for which the coefficient of x2 in the expansion

(1 + x)m is 6

Miscellaneous Exercise [Pages 175 - 176]

### NCERT solutions for Class 11 Mathematics Chapter 8 Binomial Theorem Miscellaneous Exercise [Pages 175 - 176]

Miscellaneous Exercise | Q 1 | Page 175

Find ab and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.

Miscellaneous Exercise | Q 1 | Page 175

Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.

Miscellaneous Exercise | Q 3 | Page 175

Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.

Miscellaneous Exercise | Q 4 | Page 175

If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.

[Hint: write an = (a – b b)n and expand]

Miscellaneous Exercise | Q 5 | Page 175

Evaluate (sqrt3  +sqrt2)^6 - (sqrt3 - sqrt2)^6

Miscellaneous Exercise | Q 6 | Page 175

Find the value of (a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4

Miscellaneous Exercise | Q 7 | Page 175

Find an approximation of (0.99)5 using the first three terms of its expansion.

Miscellaneous Exercise | Q 8 | Page 175

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (root4 2 + 1/ root4 3)^n " is " sqrt6 : 1

Miscellaneous Exercise | Q 9 | Page 176

Expand using Binomial Theorem (1+ x/2 - 2/x)^4, x != 0

Miscellaneous Exercise | Q 10 | Page 176

Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.

## Solutions for Chapter 8: Binomial Theorem

Exercise 8.1Exercise 8.2Miscellaneous Exercise

## NCERT solutions for Class 11 Mathematics chapter 8 - Binomial Theorem

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Concepts covered in Class 11 Mathematics chapter 8 Binomial Theorem are Binomial Theorem for Positive Integral Indices, General and Middle Terms, Introduction of Binomial Theorem, Proof of Binomial Therom by Pattern, Proof of Binomial Therom by Combination, Rth Term from End, Simple Applications of Binomial Theorem.

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