(2 + 3)^-1 x (2^-1 + 3^-1) is equal to :

1. 6

2. -6

3. $\dfrac{1}{6}$

4. $-\dfrac{1}{6}$

Statement 1: $\Big(\dfrac{3}{4}\Big)^{-4} \times \Big(\dfrac{3}{4}\Big)^{-5} = \Big(\dfrac{3}{4}\Big)^{3x}$

⇒ x = -1

Statement 2: $\Big(\dfrac{3}{4}\Big)^{-4 - 5} = \Big(\dfrac{3}{4}\Big)^{3x}$

⇒ 3x = -9

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Assertion (A): (3^-7 ÷ 3^-10) x 3^-5 = $\dfrac{1}{9}$.

Reason (R): $\dfrac{1}{3^7} \times 3^{10} \times \dfrac{1}{3^5}$.

1. A is true, but R is false.

2. A is false, but 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.

Assertion (A): (1³ + 2³ + 3³)$^\frac{1}{2}$ = x, then x = $\sqrt{1} + \sqrt{8} + \sqrt{27}$.

Reason (R): x = (1 + 8 + 27)$^\frac{1}{2} = 36^\frac{1}{2} = 6$

1. A is true, but R is false.

2. A is false, but 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.