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
Class 11 Maths Chapter 8 Binomial Theorem Solutions
- Download Exercise 8.1
- Download Exercise 8.2
- Download Miscellaneous Exercise 8
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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.
- 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.
- 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.