The maximum number of points of intersection of 9 straight lines drawn in a plane is
(i) 72
(ii) 36
(iii) 18
(iv) None of these

Options

A. 72
B. 36
C. 18
D. none of these

Answer

To find the maximum number of points of intersection of 9 straight lines drawn in a plane, we can use the concept of combinations. The maximum number of intersection points occurs when no two lines are parallel and no three lines meet at a single point.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the maximum number of intersection points formed by 9 straight lines. Each intersection point is formed by the crossing of two lines.

2. **Using Combinations**:
To find the number of ways to choose 2 lines from 9 lines, we use the combination formula:
\[ nC2 = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of lines (9 in this case) and \( r \) is the number of lines we want to choose (2 for intersection).

3. **Substituting Values**:
Here, \( n = 9 \) and \( r = 2 \):
\[ 9C2 = \frac{9!}{2!(9-2)!} = \frac{9!}{2! \cdot 7!} \]

4. **Simplifying the Factorials**:
We can simplify \( 9! \) as follows:
\[ 9! = 9 \times 8 \times 7! \]
Thus,
\[ 9C2 = \frac{9 \times 8 \times 7!}{2! \times 7!} \]

5. **Cancelling the Factorials**:
The \( 7! \) in the numerator and denominator cancels out:
\[ 9C2 = \frac{9 \times 8}{2!} \]

6. **Calculating \( 2! \)**:
We know that \( 2! = 2 \), so:
\[ 9C2 = \frac{9 \times 8}{2} = \frac{72}{2} = 36 \]

7. **Conclusion**:
Therefore, the maximum number of points of intersection of 9 straight lines is \( 36 \).

### Final Answer:
The maximum number of points of intersection of 9 straight lines drawn in a plane is **36** (Option ii).