Statement 1: The expression 2x⁴ - 3x² + $\dfrac{7}{\text{x}}$, x ≠ 0 has no constant term.

Statement 2: In an algebraic expression in terms of one variable, the term(s) independent of the variable is called the constant.

Which of the following options is correct?

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.

Given :

2x⁴ - 3x² + $\dfrac{7}{\text{x}}$

A constant term is a term that does not contain the variable in this case, x.

Thus, the expression contains no constant term.

So, statement 1 is true.

In an algebraic expression in terms of one variable, the term(s) independent of the variable is called the constant.

This is a standard definition in algebra: a constant term is the part of the expression that does not change with the variable i.e., it is independent of the variable.

So, statement 2 is true.

Hence, option 1 is the correct option.