Revision Notes: Binomial Theorem

# Binomial Theorem Class 11 Notes Maths Chapter 7

``` Page 1

KEY POINTS
? If n is a natural number and a, b are any numbers.
1 2 2
0 1 2
0
( ) ............
,
n n n n n n n n n
n
n
n n r r
r
r
a b c a c a b c a b c b
c a b n N
? ?
?
?
? ? ? ? ? ?
? ?
?
? Tr + 1 = General term
0
n n r r
r
c a b r n
?
? ? ?
? Total number of terms in (a + b)
n
is (n + 1).
? If n is even, then in the expansion of ( )
n
a b ? , middle term is
1
2
th
n ? ?
?
? ?
? ?
term i,e
2
2
th
n ? ? ?
? ?
? ?
terms.
? If n is odd, then in the expansion of (a + b)
n
, middle terms are
1
2
th
n ? ? ?
? ?
? ?
and
3
2
th
n ? ? ?
? ?
? ?
? In (a + b)
n
, r
th
term from the end is same as ( n – r + 2)
th
term
from the beginning.
Page 2

KEY POINTS
? If n is a natural number and a, b are any numbers.
1 2 2
0 1 2
0
( ) ............
,
n n n n n n n n n
n
n
n n r r
r
r
a b c a c a b c a b c b
c a b n N
? ?
?
?
? ? ? ? ? ?
? ?
?
? Tr + 1 = General term
0
n n r r
r
c a b r n
?
? ? ?
? Total number of terms in (a + b)
n
is (n + 1).
? If n is even, then in the expansion of ( )
n
a b ? , middle term is
1
2
th
n ? ?
?
? ?
? ?
term i,e
2
2
th
n ? ? ?
? ?
? ?
terms.
? If n is odd, then in the expansion of (a + b)
n
, middle terms are
1
2
th
n ? ? ?
? ?
? ?
and
3
2
th
n ? ? ?
? ?
? ?
? In (a + b)
n
, r
th
term from the end is same as ( n – r + 2)
th
term
from the beginning.

? r
th
term from the end in (b + a)
n
= r
th
term from the beginning in (a + b)
n

? In (1 + x)
n
, coefficient of x
r
is
n
Cr
? Some particular cases:
? ?
0
1
n
n
n r
r
r
x c x
?
? ?
?
? ?
0
1 ( 1 )
n
n
r n r
r
r
x c x
?
? ? ?
?
? Some properties of Binomial coefficients:
n
C0 +
n
C1 +
n
C2 + ... +
n
Cn = 2
n
n
C0 –
n
C1 +
n
C2 –
n
C3 + ... + (–1)
nn
Cn = 0
n
C0 +
n
C2 +
n
C4 + ... =
n
C1 +
n
C3 + n
C
5 + ... = 2
n–1

```

## Mathematics (Maths) for JEE Main & Advanced

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## FAQs on Binomial Theorem Class 11 Notes Maths Chapter 7

 1. What is the binomial theorem in JEE?
Ans. The binomial theorem in JEE is a mathematical formula that allows us to expand a binomial expression raised to a power. It is commonly used to simplify complex algebraic expressions and solve problems related to combinatorics and probability.
 2. How is the binomial theorem used in JEE exams?
Ans. The binomial theorem is often used in JEE exams to solve problems involving the expansion of binomial expressions, finding specific terms in a binomial expansion, and solving equations involving binomial coefficients. It is an important tool in algebraic manipulation and helps in solving complex mathematical problems efficiently.
 3. What are binomial coefficients and how are they related to the binomial theorem?
Ans. Binomial coefficients are the numerical coefficients that appear in the expansion of a binomial expression. They represent the number of ways to choose a certain number of elements from a set. In the binomial theorem, the binomial coefficients are determined by Pascal's triangle and play a crucial role in expanding binomial expressions.
 4. Can the binomial theorem be used to find the coefficients of a binomial expansion?
Ans. Yes, the binomial theorem can be used to determine the coefficients of a binomial expansion. The formula provides a systematic way to calculate each term of the expansion, including the coefficients. By using the binomial coefficients and the powers of the binomial expression, we can easily determine the coefficients of the expanded expression.
 5. Are there any applications of the binomial theorem in real-life scenarios?
Ans. Yes, the binomial theorem has several real-life applications. It is used in probability theory to calculate the probability of certain events, such as the probability of obtaining a certain number of heads in a series of coin flips. It is also used in finance and economics to model and calculate compound interest, investment returns, and loan payments. The binomial theorem provides a powerful tool for solving various problems in different fields.

## Mathematics (Maths) for JEE Main & Advanced

210 videos|446 docs|143 tests

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