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​[(0.1)2−(0.01)2]0.0001+2\frac{[(0.1)^2 - (0.01)^2]}{0.0001} + 20.0001[(0.1)2−(0.01)2]​+2 is equal to :​
Question

[(0.1)2(0.01)2]0.0001+2\frac{[(0.1)^2 - (0.01)^2]}{0.0001} + 2 is equal to :​

A.

101

B.

1.01

C.

100

D.

1.10

Correct option is A

Given:

[(0.1)2(0.01)2]0.0001+2\frac{[(0.1)^2 - (0.01)^2]}{0.0001} + 2

Formula Used:

​​a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

​​Solution:

[(0.1)2(0.01)2]0.0001+2\frac{[(0.1)^2 - (0.01)^2]}{0.0001} + 2

[(0.1+0.01)(0.10.01)]0.0001+2\frac{[(0.1+0.01)(0.1-0.01)]}{0.0001} + 2

[(0.11)(0.09)]0.0001+2\frac{[(0.11)(0.09)]}{0.0001} + 2

0.00990.0001+2 \frac{0.0099}{0.0001} + 2

= 99 + 2 

= 101

Thus, the correct answer is (a).

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