Assertion (A): The number obtained on rationalizing the denominator of $\dfrac{1}{\sqrt{5} - 2}$ is $2 + \sqrt{5}$.

Reason (R): If the product of two irrational numbers is rational, then each one is called the rationalizing factor of the other.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false.

Assertion (A): Each of the numbers $\sqrt[3]{2}, \sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{5}, \sqrt[3]{6}, \sqrt[3]{7}$ is irrational.

Reason (R): The cube roots of all natural numbers is irrational.

1. A is true, R is false

2. Both A and R are true

3. A is false, R is true

4. Both A and R are false.

Four rational numbers p, q, r and s are such that q is the reciprocal of p and s is the reciprocal of r. The value of the expression $\Big([p + \dfrac{1}{q}] ÷ [r + \dfrac{1}{s}]\Big) ÷ \Big([s + \dfrac{1}{r}] ÷ [q + \dfrac{1}{p}]\Big)$ is equal to:

1. 1

2. 0

3. pr

4. $\dfrac{s}{q}$

$0.6 + 0.\overline{7} + 0.4\overline{7}$ is equal to:

1. $\dfrac{155}{90}$

2. $\dfrac{147}{90}$

3. $\dfrac{167}{90}$

4. none of these