Two rational numbers between $-\dfrac{3}{7} \text{ and } -\dfrac{1}{7}$ is :

1. $\dfrac{4}{14}, \dfrac{3}{14}$

2. $-\dfrac{4}{14}, \dfrac{3}{14}$

3. $\dfrac{4}{14}, -\dfrac{3}{14}$

4. $-\dfrac{4}{14}, -\dfrac{3}{14}$

The correct ascending order of $\sqrt{3} , \sqrt[3]{6}, \sqrt[4]{7}$ is :

1. $\sqrt[3]{6}, \sqrt[4]{7}, \sqrt{3}$

2. $\sqrt[4]{7}, \sqrt{3}, \sqrt[3]{6}$

3. $\sqrt{3}, \sqrt[4]{7}, \sqrt[3]{6}$

4. $\sqrt[3]{6}, \sqrt{3}, \sqrt[4]{7}$

What is the pure surd for $5\sqrt[3]{2}$ ?

1. $\sqrt[3]{125}$

2. $\sqrt[3]{150}$

3. $\sqrt[3]{250}$

4. $\sqrt[3]{1000}$

Case Study

The union of the set of rational numbers (Q) and irrational numbers (P) form the set of real numbers (R). Rational numbers are the set of numbers which can be written in the form of $\dfrac{a}{b}$, where a and b are integers and b is not equal to zero. The decimal expansion of a rational number is either terminating or non-terminating repeating. The number which cannot be expressed in the form $\dfrac{a}{b}$ are called irrational numbers. The decimal expansion of irrational numbers is non-terminating non-repeating.

Based on this information, answer the following questions:

1. Every rational number is:
   (a) a natural number
   (b) a whole number
   (c) an integer
   (d) a real number

2. Every real number is:
   (a) an integer
   (b) a rational number
   (c) an irrational number
   (d) either a rational number or an irrational number.

3. The sum of two irrationals is:
   (a) irrational
   (b) rational
   (c) either rational or irrational
   (d) neither rational or irrational.

4. The product of a rational and irrational number is:
   (a) an irrational number
   (b) a rational number
   (c) either a rational number or an irrational number
   (d) neither a rational number nor an irrational number.

5. The number of irrational number is:
   (a) finite
   (b) infinite
   (c) neither finite or infinite
   (d) none of these.