Statement 1: Lines `3x+4y+6=0,sqrt(2)x+sqrt(3)y+2sqrt(2)=0` and `4x+7y+8=0` are concurrent.
Statement 2 : If three lines are concurrent then determinant of coefficients should be non-zero.

Options

A. Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True and 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

Answer

To determine whether the given statements about the lines are true or false, we will analyze the equations of the lines and calculate the determinant of their coefficients.

### Step-by-Step Solution:

1. **Identify the equations of the lines:**
The three lines given are:
- Line 1: \(3x + 4y + 6 = 0\)
- Line 2: \(\sqrt{2}x + \sqrt{3}y + 2\sqrt{2} = 0\)
- Line 3: \(4x + 7y + 8 = 0\)

2. **Write the coefficients in matrix form:**
The coefficients of the lines can be represented in a matrix as follows:
\[ \begin{bmatrix} 3 & 4 & 6 \\ \sqrt{2} & \sqrt{3} & 2\sqrt{2} \\ 4 & 7 & 8 \end{bmatrix} \]

3. **Calculate the determinant of the coefficient matrix:**
To check if the lines are concurrent, we need to calculate the determinant of the coefficient matrix. The determinant can be calculated using the formula for a 3x3 matrix:
\[ \text{Det} = a(ei - fh) - b(di - fg) + c(dh - eg) \]
where \(a, b, c\) are the first row coefficients, \(d, e, f\) are the second row coefficients, and \(g, h, i\) are the third row coefficients.

Here, we have:
- \(a = 3\), \(b = 4\), \(c = 6\)
- \(d = \sqrt{2}\), \(e = \sqrt{3}\), \(f = 2\sqrt{2}\)
- \(g = 4\), \(h = 7\), \(i = 8\)

The determinant can be calculated as:
\[ \text{Det} = 3(\sqrt{3} \cdot 8 - 2\sqrt{2} \cdot 7) - 4(\sqrt{2} \cdot 8 - 2\sqrt{2} \cdot 4) + 6(\sqrt{2} \cdot 7 - \sqrt{3} \cdot 4) \]

Now, we will compute each term:
- First term: \(3(8\sqrt{3} - 14\sqrt{2})\)
- Second term: \(4(8\sqrt{2} - 8\sqrt{2}) = 0\)
- Third term: \(6(7\sqrt{2} - 4\sqrt{3})\)

Therefore, we have:
\[ \text{Det} = 3(8\sqrt{3} - 14\sqrt{2}) + 0 + 6(7\sqrt{2} - 4\sqrt{3}) \]

4. **Simplifying the determinant:**
Combine like terms:
\[ \text{Det} = 24\sqrt{3} - 42\sqrt{2} + 42\sqrt{2} - 24\sqrt{3} = 0 \]

5. **Conclusion about the statements:**
Since the determinant is equal to 0, the three lines are concurrent, which confirms that Statement 1 is true.

For Statement 2, it states that if three lines are concurrent, then the determinant of the coefficients should be non-zero. This is false because we have shown that the determinant must be zero for the lines to be concurrent.

### Final Answer:
- Statement 1: True
- Statement 2: False