#### Chapters

Chapter 2: Relations and Functions

Chapter 3: Trigonometric Functions

Chapter 4: Principle of Mathematical Induction

Chapter 5: Complex Numbers and Quadratic Equations

Chapter 6: Linear Inequalities

Chapter 7: Permutations and Combinations

Chapter 8: Binomial Theorem

Chapter 9: Sequences and Series

Chapter 10: Straight Lines

Chapter 11: Conic Sections

Chapter 12: Introduction to Three Dimensional Geometry

Chapter 13: Limits and Derivatives

Chapter 14: Mathematical Reasoning

Chapter 15: Statistics

Chapter 16: Probability

## Chapter 8: Binomial Theorem

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

Expand the expression (1– 2*x*)^{5}

Expand the expression (1– 2*x*)^{5}

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

Expand the expression (2*x* – 3)^{6}

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

Expand `(x + 1/x)^6`

Using Binomial Theorem, evaluate (96)^{3}

Using Binomial Theorem, evaluate (102)^{5}

Using Binomial Theorem, evaluate (101)^{4}

Using Binomial Theorem, evaluate (99)^{5}

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

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

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

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

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

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

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

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

Find the coefficient of* a*^{5}*b*^{7} in (*a* – 2*b*)^{12}

Write the general term in the expansion of (*x*^{2} – *y*)^{6}

Write the general term in the expansion of (*x*^{2} – *yx*)^{12}, *x* ≠ 0

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

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

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

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

In the expansion of (1 + *a*)^{m + n}, prove that coefficients of *a*^{m} and *a*^{n} are equal.

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*.

Prove that the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n} is twice the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n}^{–1 }.

Find a positive value of *m* for which the coefficient of *x*^{2} in the expansion

(1 + *x*)^{m} is 6

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

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

Find *a* if the coefficients of *x*^{2} and *x*^{3} in the expansion of (3 + *ax*)^{9} are equal.

Find the coefficient of *x*^{5} in the product (1 + 2*x*)^{6} (1 – *x*)^{7} using binomial theorem.

If* a* and *b* are distinct integers, prove that *a* – *b* is a factor of *a*^{n} – *b*^{n}, whenever *n* is a positive integer.

[**Hint:** write *a*^{n} = (*a* –* b *+ *b*)^{n} and expand]

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

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

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

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`

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

Find the expansion of (3x^{2} – 2ax + 3a^{2})^{3} using binomial theorem.

## Chapter 8: Binomial Theorem

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

NCERT solutions for Class 11 Mathematics chapter 8 (Binomial Theorem) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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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.

Using NCERT Class 11 solutions Binomial Theorem exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

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