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 number $0.\overline{25}$ is equal to

1. $\dfrac{65}{99}$

2. $\dfrac{37}{99}$

3. $\dfrac{5}{9}$

4. $\dfrac{25}{99}$

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.

Assertion (A): $-\dfrac{2}{7}$ is a rational number.

Reason (R): Any number that can be expressed in the form $\dfrac{p}{q}$ is a rational number.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).