NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem are part of NCERT Exemplar Class 11 Maths. Here we have given NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem. https://www.cbselabs.com/ncert-exemplar-problems-class-11-mathematics-chapter-8-binomial-theorem/

## NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem

**Short Answer Type Questions:**

Expanding Binomial Calculator is a free online tool that lets you solve the expansion of a binomial in the blink of an eye.

Q1. Find the term independent of x, where xâ‰ 0, in the expansion of \({ \left( \frac { 3{ x }^{ 2 } }{ 2 } -\quad \frac { 1 }{ 3x } Â \right) Â }^{ 15 }\)

**Q2. If the term free from x is the expansion of Â \({ \left( \sqrt { x } -\frac { k }{ { x }^{ 2 } } Â \right) Â }^{ 10 }\) is 405, then find theÂ value of k.**

**Sol:**Â Given expansion isÂ \({ \left( \sqrt { x } -\frac { k }{ { x }^{ 2 } } Â \right) Â }^{ 10 }\)

**Q3. Find the coefficient of x in the expansion of (1 – 3x + 1x ^{2})( 1 -x)^{16}.**

**Sol:Â **(1 – 3x + 1x^{2})( 1 -x)^{16}

**Q4.Â Find the term independent of x in the expansion ofÂ \({ \left( 3x-\frac { 2 }{ { x }^{ 2 } } Â \right) Â }^{ 15 }\)**

**Sol: **Given ExpressionÂ \({ \left( 3x-\frac { 2 }{ { x }^{ 2 } } Â \right) Â }^{ 15 }\)

**Q5. Find the middle term (terms) in the expansion of**

**Q6. Find the coefficient of x ^{15} in the expansion ofÂ \({ \left( x-{ x }^{ 2 }\quad Â \right) Â }^{ 10 }\)**

**Sol:** Given expression is Â **Â **\({ \left( x-{ x }^{ 2 }\quad Â \right) Â }^{ 10 }\)

**Q7. Find the coefficient of \(\frac { 1 }{ { x }^{ 17 } } \) in the expansion ofÂ \({ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \quad Â \right) Â }^{ 15 } \)**

**Q8. Find the sixth term of the expansion (y ^{1/2} + x^{1/3})^{n}, if the binomial coefficient of the third term from the end is 45.**

>

**Q9. Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x) ^{18} are equal.**

**Q10. If the coefficient of second, third and fourth terms in the expansion of (1 + x) ^{2}” are in A.P., then show that 2n^{2} – 9n + 7 = 0.**

**Q11. Find the coefficient of x ^{4} in the expansion of (1 + x + x^{2} + x^{3})^{11}.**

**Long Answer Type Questions**

**Q12. If p is a real number and the middle term in the expansion \({ \left( \frac { p }{ 2 } +2\quad \right) }^{ 8 } \) is 1120, then find the value of p.**

**Q15. In the expansion of (x + a) ^{n}, if the sum of odd term is denoted by 0 and the sum of even term by Then, prove that**

**Q17. Find the term independent ofx in the expansion of (1 +x + 2x ^{3})\({ \left( \frac { 3 }{ 2 } { x }^{ 2 }-\frac { 1 }{ 3x } \quad \quad Â \right) Â }^{ 9 } \)**

**Objective Type Questions**

**Q18. The total number of terms in the expansion of (x + a) ^{100} + (x – a)^{100} after simplification is**

(a) 50

(b) 202

(c) 51

(d) none of these

**Q19. If the integers r > 1, n > 2 and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x) ^{2n} are equal, then**

**(a) n = 2rÂ Â Â Â Â Â Â Â Â Â Â Â Â**

**(b) n = 3rÂ Â Â Â Â Â Â Â Â Â Â Â**

**(c) n = 2r + 1Â Â Â Â Â Â Â**

**(d) none of these**

**Q20. The two successive terms in the expansion of (1 + x) ^{24} whose coefficients are in the ratio 1 : 4 are
(a) 3^{rd} and 4^{th} **

**(b) 4**

^{th}and 5^{th}**(c) 5**

^{th}and 6^{th}**(d) 6**

^{th}and 7^{th}**Q21. The coefficients of x ^{n} in the expansion of (1 + x)^{2n} and (1 + x)^{2n} ~^{1} are in the ratio**

**(a) 1 : 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â**

**(b) 1 : 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â**

**(c) 3 : 1**

**(d) 2:1**

**Q22. If the coefficients of 2 ^{nd}, 3^{rd} and the 4^{th} terms in the expansion of (1 + x)^{n} are in A.P., then the value of n is**

(a) 2 Â Â Â Â Â Â

**(b) 7Â**

**(c) 11 Â Â Â Â Â Â Â Â**

**(d) 14**

**Q23. If A and B are coefficients of Â x ^{n Â Â }in the expansions of (1 + x)^{2n} and (1 + x)^{2n}–^{1 }**

^{Â }

**respectively, then A/B Â equals to**

## NCERT Exemplar Class 11 Maths Solutions

- Chapter 1 Sets
- 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 Sequence 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

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