The value of x for the inequation 3x + 5 < 5x + 13, x ∈ Z is :

1. x > 1

2. x < 1

3. x = 1

4. x ≥ 1

The real number lines for two inequations A and B are as given below, A ∩ B is :

$-\dfrac{3}{2} \le -\dfrac{2x}{3}$ where x ∈ R.

Assertion (A): The largest value of x is $\dfrac{9}{4}$.

Reason (R): When the signs of both the sides of an inequalities are changed, the sign of inequality reverses.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is the correct reason for A.

4. Both A and R are true and R is the incorrect reason for A.

Inequation 5 - 2x ≥ x - 10, where x ∈ N (Natural numbers)

Assertion (A): 5 - 2x ≥ x - 10 ⇒ -3x ≥ -15 ⇒ x ≥ 5

∴ Solution set = {5, 6, 7, 8, ……….}

Reason (R): 5 - 2x ≥ x - 10 ⇒ 5 + 10 ≥ 3x ⇒ x ≤ 5

∴ Solution set = {1, 2, 3, 4, 5}

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.