Chapter 8 – Binomial Theorem (Ex – 8.1)

Binomial Theorem (Ex – 8.1)

Expand each of the expressions in Exercises 1 to 5.

Question 1.
(1−2x)⁵

Solution.

Question 2.
(2/x−x/2)⁵

Solution.

Question 3.
(2x−3)⁶

Solution.

Question 4.
(x/3+1/x)⁵

Solution.

Question 5.
(x+1/x)⁶

Solution.

Using binomial theorem, evaluate each of the following

Question 6.
(96)³

Solution.

Question 7.
(102)⁵

Solution.

Question 8.
(101)⁴

Solution.

Question 9.
(99)⁵

Solution.

Question 10.
Using Binomial Theorem, indicate which number is larger(1.1)10000 or 1000.

Solution.
Splitting 1.1 and using binomial theorem to write the first few terms we have

Question 11.

Solution.
By binomial theorem, we have

Question 12.

Solution.
By using binomial theorem, we have

Question 13.
Show that 9ⁿ⁺¹−8n−9 is divisible by 64, whenever n is a positive integer.

Solution.
We have to prove that 9ⁿ⁺¹−8n−9=64k

Question 14.

Solution.
We have,