In a plane there are 37 straight lines, of which 13 passes through the point A and 11 passes through point B. Besides, no three lines passes through one point no line passes through both points A and B and no two are parallel, then find the number of points of intersection of the straight line.

Options

A. 535
B. 601
C. 728
D. 963

Explanation

To solve the problem, we need to find the total number of points of intersection formed by 37 straight lines in a plane, given specific conditions about the lines passing through points A and B.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Total lines = 37
- Lines through point A = 13
- Lines through point B = 11
- No three lines intersect at a single point.
- No line passes through both points A and B.
- No two lines are parallel.

2. **Calculate the Number of Lines Not Passing Through A or B:**
\[ \text{Lines not through A or B} = 37 - 13 - 11 = 13 \]
Let’s denote these lines as N lines.

3. **Calculate the Intersections Between Lines Through A and B:**
- Lines through A can intersect with lines through B.
- The number of intersection points between lines through A and lines through B is given by:
\[ \text{Intersections (A and B)} = 13 \times 11 = 143 \]

4. **Calculate the Intersections Between N Lines and Lines Through A and B:**
- Each N line can intersect with each line through A and each line through B.
- The number of intersection points between N lines and lines through A is:
\[ \text{Intersections (N and A)} = 13 \times 13 = 169 \]
- The number of intersection points between N lines and lines through B is:
\[ \text{Intersections (N and B)} = 13 \times 11 = 143 \]

5. **Calculate Total Intersections from N Lines:**
- The total intersections from N lines with A and B lines is:
\[ \text{Total (N with A and B)} = 169 + 143 = 312 \]

6. **Calculate the Intersections Among N Lines:**
- The number of intersection points among the N lines can be calculated using combinations:
\[ \text{Intersections (N with N)} = \binom{13}{2} = \frac{13 \times 12}{2} = 78 \]

7. **Include Intersections Between A and B:**
- The lines through points A and B also create an intersection point:
\[ \text{Intersections (A and B)} = 2 \]

8. **Calculate the Total Number of Intersection Points:**
- Now, we sum all the intersection points calculated:
\[ \text{Total Intersections} = 143 + 312 + 78 + 2 = 535 \]

### Final Answer:
The total number of points of intersection of the straight lines is **535**.