State True or False :

(i) There exists a rational number which is neither positive nor negative.

(ii) Every rational number has a multiplicative inverse.

(iii) Every rational number when expressed in its standard form has its denominator greater than the numerator.

(iv) The sum of a rational number and its additive inverse is always

(v) The product of a rational number and its multiplicative inverse is always

(vi) Any two equivalent rational numbers have the same standard form.

(vii) The product of any two rational numbers is also a rational number.

(viii) A rational number when divided by another rational number always gives a rational number.

(ix) Every rational number can be represented on a number line.

(x) The rational numbers smaller than a given rational number $\dfrac{p}{q}$ lie to the left of $\dfrac{p}{q}$.

(i) True
Reason — Zero (0) is a rational number that is neither positive nor negative.

(ii) False
Reason — While most rational numbers have a multiplicative inverse, zero (0) does not, because division by zero is undefined.

(iii) False
Reason — In standard form, the denominator must be positive, but it can be smaller than the numerator (for example, $\dfrac{5}{2}$ is in standard form).

(iv) The sum of a rational number and its additive inverse is always 0.

(v) The product of a rational number and its multiplicative inverse is always 1.

(vi) True
Reason — Equivalent rational numbers like $\dfrac{2}{4}$ and $\dfrac{3}{6}$ both reduce to the same standard form, which is $\dfrac{1}{2}$.

(vii) True
Reason — According to closure property of multiplication for rational numbers, the product of any two rational numbers is also a rational number.

(viii) False
Reason — A rational number divided by zero does not give a rational number, as division by zero is undefined.

(ix) True
Reason — Every rational number corresponds to a unique point on the number line.

(x) True
Reason — On a number line, values decrease as you move to the left; therefore, all numbers smaller than $\dfrac{p}{q}$ lie to its left.