In this chapter, we provide NCERT Exemplar Problems Solutions for Class 11 Maths Chapter 8 Binomial Theorem for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Exemplar Problems Solutions for Class 11 Maths Chapter 8 Binomial Theorem pdf, free NCERT Exemplar Problems Solutions for Class 11 Maths Chapter 8 Binomial Theorem book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 11 |

Subject | Maths |

Chapter | Chapter 8 |

Chapter Name | Binomial Theorem |

Category | NCERT Exemplar |

## NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem

**Short Answer Type Questions:**

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

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

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

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

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

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

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

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

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

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

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

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**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 } +2quad 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 right) }^{ 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 = 2r**

**(b) n = 3r**

**(c) n = 2r + 1**

**(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 : 2**

**(b) 1 : 3**

**(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

**(b) 7**

**(c) 11**

**(d) 14**

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

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

**All Chapter NCERT Exemplar Problems Solutions For Class 11 Maths**

—————————————————————————–**All Subject NCERT Exemplar Problems Solutions For Class 11**

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