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NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem

June 18, 2022 by LearnCBSE Online

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.

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 \({ \left( \frac { 3{ x }^{ 2 } }{ 2 } -\quad \frac { 1 }{ 3x }  \right)  }^{ 15 }\)

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 1

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 \({ \left( \sqrt { x } -\frac { k }{ { x }^{ 2 } }  \right)  }^{ 10 }\)

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 2
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 3

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 4

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

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 5

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 6
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 7

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

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 8

Q7. Find the coefficient of \(\frac { 1 }{ { x }^{ 17 } } \) in the expansion of \({ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \quad  \right)  }^{ 15 } \)
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 9

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.

> NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 10

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.

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 11

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.

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 12

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 13

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.

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 14
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 15
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 16
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 17

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 18
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 19
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 20
Q17. Find the term independent ofx in the expansion of (1 +x + 2x 3 )\({ \left( \frac { 3 }{ 2 } { x }^{ 2 }-\frac { 1 }{ 3x } \quad \quad  \right)  }^{ 9 } \)

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 21

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 22

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 23

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 24

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 25
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 26

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 27

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

NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 28
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 29
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 30
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 31
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 32
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 33
NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem Img 34

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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