ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Solutions Chapter-9. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1,  Exe-2, Exe-3 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

## ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Ch-9

 Class: 11th Subject: Mathematics Chapter  : Ch-9 Binomial Theorem of Section -A
 Board ISC Writer ML Aggarwal Publications APC Arya Publications 2020-21

-: Select Topics :-

Exe-9.1,

Exe-9.2,

Exe-9.3,

Chapter Test

### ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Ch-9

#### Introduction to the Binomial Theorem

The Binomial Theorem is the method of expanding an expression which has been raised to any finite power. A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc.

Binomial Expression: A binomial expression is an algebraic expression which contains two dissimilar terms. Ex: a + b, a3 + b3, etc.

Binomial Expansion

Important points to remember:

• The total number of terms in the expansion of (x+y)n  are (n+1)
• The sum of exponents of x and y is always n.
• nC0, nC1, nC2, … .., nCn are called binomial coefficients and also represented by C0, C1, C2, ….., Cn
• The binomial coefficients which are equidistant from the beginning and from the ending are equal i.e. nC= nCn, nC= nCn-1 , nC= nCn-2 ,….. etc.

#### Binomial theorem

Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form

The theorem is useful in algebra as well as for determining permutations and combinations and probabilities. For positive integer exponents, n, the theorem was known to Islamic and Chinese mathematicians of the late medieval period.

#### Binomial Expansions and Series

The binomial formula in statistics is mostly used for counting and for calculating probabilities in experiments. A very similar technique, called binomial series expansion, is used in calculus for rewriting complicated functions into a simpler (binomial) form.

Exe-9.1

### ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Ch-9

Question 1:

Find the number of terms in the expression of the following :

(i) ………..

(ii)…………

(iii)………….

Question 2:

…………………..

………………….

…………………..

Question 15:

Prove that ​$$\sum_{r=0}^{n}3^{r}C_{r}^{n} = 4^{n}$$​.

### Exe-9.2

Binomial Theorem ISC Class-11 Maths Understanding Ch-9

Question 1:

Write the general term in the expansion of

(i) (x2 – y)6

(ii) (x2 – xy)12

(iii) ……………

Question 2:

…………………..

……………………

…………………..

Question 30:

If the coefficient of ………………….. prove that n² – n (4r + 1) + 4r² – 2 = 0

Exe-9.3

### ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Ch-9

Question 1:

Find the coefficient of x7 in ………………………. if these coefficient are equal , find the relation between a and b.

Question 2:

………………….

…………………

………………….

Question 7:

If n is any positive integer, show that the integer part of  ………………….. show that (λ + f) (1 – f) = 1.

### Chapter Test

ML Aggarwal Binomial Theorem ISC Class-11 Maths Understanding Ch-9

Question 1:

Using Binomial Theorem, expand the following :

(i) (3x – 2y)5

(ii) …………….

(iii)……………

Question 2:

…………………..

…………………….

…………………….

Question 15:

If three consecutive coefficient in the expansion of (1 + x) …………………………. 33 : 110, find n.

-: End of Binomial Theorem ISC Class-11 ML Aggarwal Maths Understanding Chapter-9 Solution :-

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