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.

Assertion (A): -10 + π is an irrational number.

Reason (R): Sum of a non-zero rational number and an irrational number is an irrational 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).

Assertion (A): $0.\overline{36}$ is an irrational number.

Reason (R): Any real number that can be expressed in the form of $\dfrac{p}{q}$ where p, q are integers, q ≠ 0 and p, q have no common factor except 1 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).