The product $\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}$ equals

1. $\sqrt{2}$

2. 2

3. $\sqrt[12]{2}$

4. $\sqrt[12]{32}$

The value of $\sqrt[4]{(81)^{-2}}$ is

1. $\dfrac{1}{9}$

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

3. 9

4. $\dfrac{1}{81}$

Which of the following is equal to x?

Consider the following two statements.

Statement 1: 3^m + 2ⁿ = 5^{m + n}

Statement 2: a^m + bⁿ = (a + b)^{m + n}, where a, b, m, n are positive integers.

Which of the following is valid?

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.