Which of the following do not give rearrangement of carbocation in the additin reaction of alkene?

Options

A. `Br_(2)//CCI_(4)`
B. HBr
C. `HBr//H_(2)O_(2),hv`
D. `OSO_(4)`

Explanation

To determine which of the following do not give rearrangement of carbocation in the addition reaction of alkene, we will analyze each option based on the mechanism of the reaction involved.

### Step-by-Step Solution:

**Step 1: Analyze Option A (Bromine in CCl4)**
- When an alkene reacts with bromine in the presence of CCl4, a cyclic bromonium ion is formed as an intermediate.
- This mechanism does not involve the formation of a carbocation; hence, there is no possibility of rearrangement.
- **Conclusion**: Option A does not give rearrangement.

**Step 2: Analyze Option B (HBr)**
- The addition of HBr to an alkene follows Markovnikov's rule, where H adds to the less substituted carbon, leading to the formation of a carbocation.
- This carbocation can rearrange to a more stable form (e.g., from a 1° to a 2° or 3° carbocation).
- **Conclusion**: Option B can undergo rearrangement.

**Step 3: Analyze Option C (HBr with Hydrogen Peroxide and Sunlight)**
- This reaction proceeds via a free radical mechanism and follows the anti-Markovnikov rule.
- Since the mechanism does not involve the formation of a carbocation, there is no rearrangement.
- **Conclusion**: Option C does not give rearrangement.

**Step 4: Analyze Option D (Osmium Tetroxide)**
- The reaction of an alkene with osmium tetroxide leads to the syn addition of hydroxyl groups (OH) to the double bond.
- This process does not involve the formation of a carbocation, so rearrangement cannot occur.
- **Conclusion**: Option D does not give rearrangement.

### Final Answer:
The options that do not give rearrangement of carbocation in the addition reaction of alkene are **A, C, and D**.