The properties which are common to both groups 1 and 17 elements in the periodic table are:

Options

A. electropositive character incrases down the groups
B. Reactivity decrases from top to bottom in these grous
C. atomic radii incrases as the atomic number increases
D. Electronegativity decreases on moving down a group

Explanation

To solve the question regarding the common properties of group 1 (alkali metals) and group 17 (halogens) elements in the periodic table, we can analyze each property mentioned in the options provided.

### Step-by-Step Solution:

1. **Identify the Groups:**
- Group 1 consists of alkali metals (e.g., Lithium, Sodium, Potassium).
- Group 17 consists of halogens (e.g., Fluorine, Chlorine, Bromine).

2. **Analyze Electropositive Character:**
- The electropositive character of alkali metals increases down the group due to the increase in atomic radius, which makes it easier to lose the outermost electron.
- This property does not apply to halogens, as they are not electropositive. However, the statement is true for alkali metals alone, so we need to consider if it applies to both groups.

**Hint:** Focus on how atomic structure affects the ability to lose or gain electrons.

3. **Reactivity Trends:**
- For alkali metals, reactivity increases down the group because they lose their outermost electron more easily as the atomic size increases.
- For halogens, reactivity decreases down the group because larger atoms are less effective at attracting electrons due to increased distance from the nucleus.

**Hint:** Compare the behavior of elements in both groups regarding their tendency to lose or gain electrons.

4. **Atomic Radius:**
- The atomic radius increases as you move down both groups. This is a common property of both alkali metals and halogens.

**Hint:** Remember that atomic radius is influenced by the number of electron shells.

5. **Electronegativity:**
- Electronegativity decreases down the group for both alkali metals and halogens. For alkali metals, as electropositivity increases, electronegativity decreases. For halogens, larger atoms have lower electronegativity.

**Hint:** Understand the relationship between electronegativity and atomic size.

### Conclusion:
Based on the analysis:
- **Correct Properties Common to Both Groups:**
- Electropositive character increases down the group (for alkali metals).
- Atomic radius increases down the group (common to both).
- Electronegativity decreases down the group (common to both).

Thus, the correct answer includes the first, third, and fourth options as common properties.

### Final Answer:
The properties which are common to both groups 1 and 17 elements in the periodic table are:
1. Atomic radius increases as the atomic number increases (True for both groups).
2. Electronegativity decreases on moving down the group (True for both groups).