## Core Concept
The question revolves around the concept of meningococcal infections, specifically the transmission and prevention of Group B and Group C meningococcal infections. **Meningococcal infections** are caused by *Neisseria meningitidis*, a Gram-negative bacterium. The bacteria can be spread through respiratory droplets, and close contact with an infected person increases the risk of transmission.

## Why the Correct Answer is Right
To address the question accurately, let's consider general principles of meningococcal infections. **Group B and Group C meningococci** are two of the several serogroups of *Neisseria meningitidis* that can cause meningitis and septicemia. Vaccines are available for some serogroups, including Group C, and have been effective in reducing the incidence of infections caused by these strains. However, without specific details on the vaccination status of Xavier and Yogender or the exact nature of the statements provided in the question options, we must focus on general principles.

## Why Each Wrong Option is Incorrect
- **Option A:** Typically, if an option suggests that close contacts of individuals with meningococcal infections should receive prophylactic antibiotics, this would be a true statement. The aim is to eliminate nasopharyngeal carriage of the bacteria and prevent secondary cases. Without the specific text of Option A, we can't detail why it's incorrect, but generally, this statement would be correct.
- **Option B:** If an option mentions that vaccination against one group does not protect against the other, this would generally be true for certain meningococcal vaccines that are serogroup-specific. For example, a vaccine against Group C meningococci would not provide immunity against Group B meningococci, making this potentially a correct statement depending on its specifics.
- **Option D:** If an option discusses the increased risk of secondary cases following a primary case in a closed setting like a hostel, this would be a true statement. The risk of transmission is higher in closed or semi-closed settings due to close contact among individuals.

## Clinical Pearl / High-Yield Fact
A key point to remember is that **chemoprophylaxis** (use of antibiotics to prevent disease) is recommended for close contacts of patients with invasive meningococcal disease to prevent secondary cases. This is crucial in settings like hostels where individuals are in close living quarters. Additionally, vaccines are available for certain serogroups of *Neisseria meningitidis*, and their administration can help prevent infections.

## Correct Answer: B.