After rationalising the denominator of $\dfrac{7}{3\sqrt3 - 2\sqrt{2}}$ , we get the denominator as

1. 13
2. 19
3. 5
4. 35

The number obtained on rationalising the denominator of ${\dfrac{1}{\sqrt{7} - 2}}$ is

1. ${\dfrac{\sqrt{7} + 2}{3}}$

2. ${\dfrac{\sqrt{7} - 2}{3}}$

3. ${\dfrac{\sqrt{7} + 2}{5}}$

4. ${\dfrac{\sqrt{7} + 2}{45}}$

The value of $1.99\overline{9}$ in the form of $\dfrac{p}{q}$, where p and q are integers and q ≠ 0, is

1. $\dfrac{19}{20}$

2. $\dfrac{1999}{1000}$

3. 2

4. $\dfrac{1}{9}$

Consider the following two statements:

Statement 1: 2^m x 3ⁿ = (2 + 3)^{m + n}, where m, n are positive integers.

Statement 2: If a is a rational number, and m, n are integers, then a^m.aⁿ = a^{m + n}

Which of the following is valid?

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.