Assertion (A) : The degree of quadratic equation is always 2 and `x^(2)-1=0` is pure quadratic equation.
Reason (R ) : An equation of the form `ax^(2)+c=0` is known as pure quadratic equation.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false
D. A is false but R is true

Answer

To solve the question, we need to analyze the assertion (A) and reason (R) provided:

**Assertion (A)**: The degree of a quadratic equation is always 2, and \( x^2 - 1 = 0 \) is a pure quadratic equation.

**Reason (R)**: An equation of the form \( ax^2 + c = 0 \) is known as a pure quadratic equation.

### Step-by-Step Solution:

1. **Understanding the Degree of Quadratic Equations**:
- A quadratic equation is defined as any equation that can be expressed in the standard form \( ax^2 + bx + c = 0 \), where \( a, b, c \) are constants and \( a \neq 0 \).
- The highest power of the variable \( x \) in this equation is 2, which means the degree of a quadratic equation is always 2.

**Hint**: Recall that the degree of a polynomial is determined by the highest exponent of the variable.

2. **Analyzing the Equation \( x^2 - 1 = 0 \)**:
- The equation \( x^2 - 1 = 0 \) can be rewritten as \( 1x^2 + 0x - 1 = 0 \).
- Here, \( a = 1 \), \( b = 0 \), and \( c = -1 \). Since it contains the term \( x^2 \) and a constant, it fits the definition of a quadratic equation.
- Since there is no linear term (the coefficient of \( x \) is 0), this equation is classified as a pure quadratic equation.

**Hint**: Identify the coefficients in the standard form of a quadratic equation to determine its type.

3. **Understanding Pure Quadratic Equations**:
- A pure quadratic equation is one that can be expressed in the form \( ax^2 + c = 0 \) where \( b = 0 \). This means it has no linear term.
- The equation \( x^2 - 1 = 0 \) can be expressed as \( 1x^2 + 0x - 1 = 0 \), which confirms it is a pure quadratic equation.

**Hint**: Check if the equation lacks the linear term to determine if it is pure.

4. **Conclusion**:
- Both the assertion (A) and the reason (R) are true.
- The reason (R) correctly explains the assertion (A) because it defines what a pure quadratic equation is.

### Final Answer:
- The assertion (A) is true, and the reason (R) is also true. The reason (R) provides a correct explanation for the assertion (A).