STATEMENT-1 : To find complete solution of a second order differential equation we need two different conditions.
and
STATEMENT-2 : An `n^(th)` order differential equation has n independent parameters.

Options

A. (a)Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. (b)Statement-1 is true, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
C. (c)Statement-1 is True, Statement-2 is False
D. (d)Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we need to analyze both statements regarding differential equations.

### Step 1: Analyze Statement 1
**Statement 1:** To find the complete solution of a second-order differential equation, we need two different conditions.

**Explanation:**
A second-order differential equation can be expressed in the form:
\[ \frac{d^2y}{dx^2} = f(x, y, \frac{dy}{dx}) \]
To find the complete solution of this equation, we typically need two initial or boundary conditions. These conditions can be:
1. The value of the function \( y \) at a certain point (initial condition).
2. The value of the first derivative \( \frac{dy}{dx} \) at that same point or another point.

Thus, Statement 1 is **True**.

### Step 2: Analyze Statement 2
**Statement 2:** An \( n^{th} \) order differential equation has \( n \) independent parameters.

**Explanation:**
An \( n^{th} \) order differential equation can be expressed as:
\[ \frac{d^n y}{dx^n} = f(x, y, \frac{dy}{dx}, \ldots, \frac{d^{n-1}y}{dx^{n-1}}) \]
To find the general solution of this equation, we will have \( n \) arbitrary constants (or parameters) in the solution. These constants arise from integrating the equation \( n \) times.

Thus, Statement 2 is also **True**.

### Step 3: Conclusion
Both statements are true, and Statement 2 provides a correct explanation for Statement 1. Therefore, the correct option is:

**Option A: Statement 1 is true and Statement 2 is true, and Statement 2 is a correct explanation of Statement 1.**