Two columns are given as shown below :
Column - I – Column - II
(a) face of a black-board – (i) two end points
(b) a line has – (ii) one end point
(c) a ray has – (iii) represents a part of a plane
(d) a line segment has – (iv) no definite length

Column-I and II are matched as:

Question

Two columns are given as shown below :
Column - I – Column - II
(a) face of a black-board – (i) two end points
(b) a line has – (ii) one end point
(c) a ray has – (iii) represents a part of a plane
(d) a line segment has – (iv) no definite length

Column-I and II are matched as:

Accepted Answer

To understand why Option 3 is the correct answer, let's analyze the relationships between the items in Column I and Column II:

1. **(a) face of a black-board – (iii) represents a part of a plane**
   - A blackboard is a flat surface, which can be considered as a part of a plane in geometric terms. It extends in two dimensions and does not have thickness, similar to a plane. Therefore, the face of a blackboard is best matched with "represents a part of a plane."

2. **(b) a line has – (iv) no definite length**
   - A line in geometry is defined as a straight one-dimensional figure having no thickness and extending infinitely in both directions. It does not have a definite length, which aligns with the description "no definite length."

3. **(c) a ray has – (ii) one end point**
   - A ray starts at a point and extends infinitely in one direction. It has one endpoint where it begins, which matches the description "one end point."

4. **(d) a line segment has – (i) two end points**
   - A line segment is a part of a line that is bounded by two distinct endpoints. It has a definite length, which is defined by the distance between these two points. Thus, it corresponds to "two end points."

Now, let's explain why the other options are incorrect:

- **Option 1: (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)**
  - This option incorrectly matches the face of a blackboard with "one end point," which is not accurate as a blackboard represents a part of a plane. It also mismatches a line with "represents a part of a plane," which is incorrect since a line extends infinitely and does not represent a plane.

- **Option 2: (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)**
  - This option incorrectly matches a line with "one end point," which is incorrect because a line extends infinitely in both directions and does not have endpoints. It also mismatches a line segment with "no definite length," which is incorrect as a line segment has a definite length.

- **Option 4: (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)**
  - This option incorrectly matches the face of a blackboard with "two end points," which is not accurate as a blackboard represents a part of a plane. It also mismatches a ray with "no definite length," which is incorrect because a ray has one endpoint.

In conclusion, Option 3 correctly matches each item in Column I with the appropriate description in Column II based on geometric definitions and properties.