Write true (T) or false (F):

(i) Every rational number has a reciprocal.

(ii) Subtraction of rational numbers is commutative.

(iii) The additive inverse of $\dfrac{1}{4}$ is -4.

(iv) $\dfrac{5}{0}$ is a rational number.

(v) 0 is the smallest rational number.

(vi) The multiplicative inverse of $\dfrac{-4}{-9}$ is $\dfrac{9}{4}$.

(vii) There are countless rational numbers between $\dfrac{2}{3} \text{ and } \dfrac{5}{6}$.

Assertion (A): Rational numbers are closed under addition and multiplication but not under subtraction.

Reason (R): For any two rational numbers a and b,

a + b is a rational number

a - b is a rational number

a × b is a rational number.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Assertion (A): For any rational numbers x, y, z, we have, x × (y + z) = x × y + x × z.

Reason (R): Rational numbers are associative under addition and multiplication.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Ramesh earns ₹ 40,000 per month. He spends $\dfrac{3}{8}$ of income on food, $\dfrac{1}{5}$ of the remaining on LIC premium and $\dfrac{1}{2}$ of the remaining on other expenses. Find how much money is left with him?

1. ₹8,000

2. ₹10,000

3. ₹15,000

4. ₹16,000