NCERT Solutions for Class 11 Maths Chapter 8

Download NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem द्विपद प्रमेय in PDF format based on latest CBSE Curriculum 2018-19 for CBSE Board, UP Board, Uttarakhand, Bihar Board, etc. who are following NCERT Books for their study.


NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

NCERT Solutions for Class 11 Maths Chapter 8

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Class 11 Maths Chapter 8 Binomial Theorem Solutions




Important Terms on Binomial Theorem

  • Binomial Expression: Any expression containing two terms combined by + or – is called Binomial expression. For example: x + 3, 2x + y, x – 4y, 4 – 100x, y – 4, etc.
  • In the expansion of (a + b)^n, the coefficient of first term = coefficient of last term, coefficient of second term = coefficient of second term from last. Thus we get that in the expansion of (a + b)^n, the terms from first term and from the last term at equal distance have the same coefficients.
  • The General Term: The term (r + 1) is called the general term of the expansion (a + b)^n because we can get different terms from this term by giving different values to r. This general term is denoted by Tr+1.



  • The Middle Term: In the expansion of (a + b)^n, the total number of terms are (n + 1). The middle term in the expansion of (a + b)^n depend on n.
    1. When n is even: Let n = 2m, where m is positive integer. The total number of terms will be 2m + 1. Hence, the middle term of the expansion (a + b)^n will be 1/2[(2m + 1) + 1], i. e. when n is even then (m + 1)th term or (n/2 + 1)th will be the middle term.
    2. When n is odd: Let n = 2m + 1, where m is a positive integer. In the expansion of (a + b)^n the total number of terms will be (m + 2). The middle term in the expansion of (a + b)^n will be (m + 1)th and (m + 2)th term or (n + 1)/2th and ((n + 3)/2th term.


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