`E` represents an element belonging to boron family.
`2E+3X_(2) to 2EX_(3) (X=F,Cl, Br, I)`

Options

A. Oxidation state of `E` in all `EX_(3)` is `+3`
B. All `EX_(3)` are predominantly ionic
C. Ti does not form `TIX_(3)` as `TI^(+1)` is more stable than `TI^(+3)`
D. There exists some `EX_(3)` for which `E` shows `+1` oxidation state.

Answer

To solve the question regarding the element `E` from the boron family and its reaction with halogens, we need to analyze the oxidation states and the nature of the compounds formed. Let's break down the solution step by step.

### Step 1: Understanding the Reaction
The reaction given is:
\[ 2E + 3X_2 \rightarrow 2EX_3 \]
where \( X \) represents halogens (F, Cl, Br, I).

### Step 2: Determine the Oxidation State of `E`
In the compound \( EX_3 \):
- Each halogen \( X \) has an oxidation state of -1.
- Since there are 3 halogens, the total contribution from halogens is \( 3 \times (-1) = -3 \).

Let the oxidation state of `E` be \( x \). The overall charge of the compound \( EX_3 \) is neutral (0). Thus, we can set up the equation:
\[ x + (-3) = 0 \]
This simplifies to:
\[ x - 3 = 0 \]
\[ x = +3 \]

### Step 3: Analyze the Options
Now, we analyze the options based on our findings:

1. **Option A**: "The oxidation state of `E` in all \( EX_3 \) is +1."
- This is incorrect because we found that the oxidation state of `E` is +3.

2. **Option B**: "All \( EX_3 \) are predominantly ionic."
- This is also incorrect. While \( AlF_3 \) is ionic, others like \( BF_3 \) and \( AlCl_3 \) are covalent.

3. **Option C**: "Tellurium does not form \( TlX_3 \) and \( Tl^+1 \) is more stable than \( Tl^+3 \)."
- This is correct. Tellurium (Te) does not form \( TeX_3 \) due to the inert pair effect, and \( Tl^+1 \) is indeed more stable than \( Tl^+3 \).

4. **Option D**: "There exists some \( EX_3 \) in which `E` shows +1 oxidation state."
- This is incorrect as we established that the oxidation state is +3 in the given compounds.

### Conclusion
The correct options based on our analysis are **Option C**.