Given lines `(x-4)/(2)=(y+5)/(4)=(z-1)/(-3) and (x-2)/(1)=(y+1)/(3)=(z)/(2)`
Statement-I The lines intersect.
Statement-II They are not parallel.

Options

A. a) Statement I is true, Statement II is also true, Statement-II is the correct explanation of Statement-I.
B. b) Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.
C. c) Statement-I is true, Statement-II is false.
D. d) Statement-I is false, Statement -II is true.

Answer

To determine whether the given lines intersect and whether they are parallel, we can follow these steps:

### Step 1: Write the equations of the lines in parametric form
The first line is given as:
\[ \frac{x-4}{2} = \frac{y+5}{4} = \frac{z-1}{-3} \]
Let \( t \) be the parameter. Then we can express the coordinates as:
\[ x = 2t + 4, \quad y = 4t - 5, \quad z = -3t + 1 \]

The second line is given as:
\[ \frac{x-2}{1} = \frac{y+1}{3} = \frac{z}{2} \]
Let \( s \) be the parameter. Then we can express the coordinates as:
\[ x = s + 2, \quad y = 3s - 1, \quad z = 2s \]

### Step 2: Set the parametric equations equal to each other
We need to find values of \( t \) and \( s \) such that:
\[ 2t + 4 = s + 2 \]
\[ 4t - 5 = 3s - 1 \]
\[ -3t + 1 = 2s \]

### Step 3: Solve the equations
From the first equation:
\[ 2t + 4 = s + 2 \implies s = 2t + 2 \]

Substituting \( s = 2t + 2 \) into the second equation:
\[ 4t - 5 = 3(2t + 2) - 1 \]
\[ 4t - 5 = 6t + 6 - 1 \]
\[ 4t - 5 = 6t + 5 \]
Rearranging gives:
\[ -5 - 5 = 6t - 4t \implies -10 = 2t \implies t = -5 \]

Now substituting \( t = -5 \) back to find \( s \):
\[ s = 2(-5) + 2 = -10 + 2 = -8 \]

### Step 4: Check if the z-coordinates match
Now, we substitute \( t = -5 \) into the z-coordinate of the first line:
\[ z = -3(-5) + 1 = 15 + 1 = 16 \]
And for \( s = -8 \) into the z-coordinate of the second line:
\[ z = 2(-8) = -16 \]

Since the z-coordinates do not match, the lines do not intersect.

### Step 5: Check if the lines are parallel
To check if the lines are parallel, we can compare the direction ratios of the lines.

For the first line, the direction ratios are \( (2, 4, -3) \).
For the second line, the direction ratios are \( (1, 3, 2) \).

To determine if they are parallel, we check if the ratios of the direction ratios are equal:
\[ \frac{2}{1} \neq \frac{4}{3} \neq \frac{-3}{2} \]
Since the ratios are not equal, the lines are not parallel.

### Conclusion
- **Statement-I**: The lines do not intersect (False).
- **Statement-II**: The lines are not parallel (True).

Thus, the correct option is:
**Option D**: Statement one is false, statement two is true.