NCERT Solutions: Exercise Miscellaneous - Binomial Theorem

# NCERT Solutions Class 11 Maths Chapter 7 - Binomial Theorem

Question 1: If a and b are distinct integers, prove that ab is a factor of anbn, whenever n is a positive integer.

[Hint: write an = (a b  + b)n and expand]

ANSWER : - In order to prove that (ab) is a factor of (anbn), it has to be proved that

anbn = k (ab), where k is some natural number

It can be written that, a = ab +  b

This shows that (ab) is a factor of (anbn), where n is a positive integer.

Question 2: Evaluate .

ANSWER : - Firstly, the expression (a  + b)6 – (ab)6 is simplified by using Binomial Theorem.

This can be done as

Question 3: Find the value of .

ANSWER : - Firstly, the expression (x  + y)4  (xy)4 is simplified by using Binomial Theorem.

This can be done as

Question 4: Find an approximation of (0.99)5 using the first three terms of its expansion.

ANSWER : - 0.99 = 1 – 0.01

Thus, the value of (0.99)5 is approximately 0.951.

Question 5: Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of

ANSWER : - In the expansion,  ,

Fifth term from the beginning

Fifth term from the end

Therefore, it is evident that in the expansion of , the fifth term from the beginning is  and the fifth term from the end is .

It is given that the ratio of the fifth term from the beginning to the fifth term from the end is . Therefore, from (1) and (2), we obtain

Thus, the value of n is 10.

Question 6: Expand using Binomial Theorem .

ANSWER : - Using Binomial Theorem, the given expression   can be expanded as

Again by using Binomial Theorem, we obtain

From (1), (2), and (3), we obtain

Question 7: Find the expansion of  using binomial theorem.

ANSWER : - Using Binomial Theorem, the given expression   can be expanded as

Again by using Binomial Theorem, we obtain

From (1) and (2), we obtain

The document NCERT Solutions Class 11 Maths Chapter 7 - Binomial Theorem is a part of the Commerce Course Mathematics (Maths) Class 11.
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## Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

## Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

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