The correct order of increasing radii are

Options

A. `Be^(2+), Mg^(2+), Na^(o+)`
B. `K^(o+), Ca^(2+), S^(2-)`
C. `O^(2-), F^(ɵ), N^(3-)`
D. `S^(2-), O^(2-), As^(3-)`

Explanation

To solve the question regarding the correct order of increasing radii among the given species, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Identify the Given Species:**
- The first option includes: Be²⁺, Mg²⁺, and Na⁺.
- The second option includes: K⁺, Ca²⁺, and S²⁻.
- The third option includes: O²⁻, F⁻, and N³⁻.
- The fourth option includes: S²⁻, O²⁻, and As³⁻.

2. **Analyze Option A: Be²⁺, Mg²⁺, Na⁺:**
- All three species are cations with different charges.
- Be²⁺ has the highest positive charge, thus it will have the smallest radius due to the greater effective nuclear charge pulling the electrons closer.
- Mg²⁺ has a lower positive charge than Be²⁺, so it will be larger than Be²⁺ but smaller than Na⁺.
- Na⁺ has the lowest positive charge, so it will have the largest radius among the three.
- **Order:** Be²⁺ < Mg²⁺ < Na⁺ (This option is correct.)

3. **Analyze Option B: K⁺, Ca²⁺, S²⁻:**
- All three species are isoelectronic with 18 electrons.
- S²⁻ has the highest negative charge, which leads to a larger radius due to electron-electron repulsion.
- K⁺ is a cation with a lower charge than S²⁻, so it will be smaller than S²⁻ but larger than Ca²⁺.
- Ca²⁺ has the highest positive charge, so it will have the smallest radius.
- **Expected Order:** Ca²⁺ < K⁺ < S²⁻ (This option is incorrect as the order is reversed.)

4. **Analyze Option C: O²⁻, F⁻, N³⁻:**
- All three species are isoelectronic with 10 electrons.
- N³⁻ has the highest negative charge, resulting in the largest radius due to increased electron-electron repulsion.
- F⁻ is smaller than N³⁻ but larger than O²⁻, which has the smallest radius due to its higher nuclear charge.
- **Expected Order:** O²⁻ < F⁻ < N³⁻ (This option is incorrect as the order is reversed.)

5. **Analyze Option D: S²⁻, O²⁻, As³⁻:**
- S²⁻ and O²⁻ are both anions, while As³⁻ is a larger anion.
- S²⁻ has a higher negative charge than O²⁻, making it larger.
- As³⁻ has more electron shells than both S²⁻ and O²⁻, making it the largest.
- **Expected Order:** O²⁻ < S²⁻ < As³⁻ (This option is incorrect as the order is reversed.)

### Conclusion:
The only correct order of increasing radii is from option A: **Be²⁺ < Mg²⁺ < Na⁺**.