Statement-1: Number of rectangles on a chessboard is `.^(8)C_(2)xx.^(8)C_(2)`.
Statement-2: To form a rectangle, we have to select any two of the horizontal lines and any two of the vertical lines.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Explanation

To solve the problem, we need to analyze the statements given about the number of rectangles that can be formed on a chessboard.

### Step-by-Step Solution:

1. **Understanding the Chessboard Structure**:
- A standard chessboard is an 8x8 grid. This means there are 8 squares along each side.
- To form rectangles, we need to consider the lines that define these squares.

2. **Counting the Lines**:
- For an 8x8 chessboard, there are 9 horizontal lines (the lines above and below the squares) and 9 vertical lines (the lines to the left and right of the squares).
- Hence, we have:
- Horizontal lines = 9
- Vertical lines = 9

3. **Choosing Lines to Form Rectangles**:
- To form a rectangle, we need to select 2 horizontal lines and 2 vertical lines.
- The number of ways to choose 2 lines from 9 lines can be calculated using the combination formula \( nCk \), which is given by:
\[ nCk = \frac{n!}{k!(n-k)!} \]

4. **Calculating the Combinations**:
- For horizontal lines:
\[ \text{Number of ways to choose 2 horizontal lines} = 9C2 = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \]
- For vertical lines:
\[ \text{Number of ways to choose 2 vertical lines} = 9C2 = 36 \]

5. **Total Number of Rectangles**:
- The total number of rectangles formed is the product of the combinations of horizontal and vertical lines:
\[ \text{Total rectangles} = 9C2 \times 9C2 = 36 \times 36 = 1296 \]

6. **Evaluating the Statements**:
- **Statement 1**: The number of rectangles on a chessboard is \( 8C2 \times 8C2 \) - This is incorrect because we should be using \( 9C2 \) instead of \( 8C2 \).
- **Statement 2**: To form a rectangle, we have to select any two of the horizontal lines and any two of the vertical lines - This is correct.

### Conclusion:
- **Statement 1 is false** and **Statement 2 is true**.