Since 90 = 2 x 3 x 3 x 5, $\dfrac{23}{90}$ is not a terminating decimal;

1. True

2. False

3. none of these

$\sqrt{27}$ is irrational and $\sqrt{3}$ is also irrational, then which of the following is rational:

1. $\sqrt{27} - \sqrt{3}$

2. $\sqrt{27} + \sqrt{3}$

3. $\sqrt{27} \times \sqrt{3}$

4. none of these

$\dfrac{2 + \sqrt{3}}{2 - \sqrt{3}} - \dfrac{2 - \sqrt{3}}{2 + \sqrt{3}}$ is equal to:

1. 4

2. $2\sqrt{3}$

3. 1

4. $8\sqrt{3}$

Statement 1: If a = $3\sqrt{3}$ and b = $\dfrac{5}{\sqrt{12}}$, then a x b is irrational.

Statement 2: a x b = $3 \sqrt{3} \times \dfrac{5}{\sqrt{12}} = \dfrac{15 \times \sqrt{3}}{2\sqrt{3}} = \dfrac{15}{2}$

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.