**Core Concept**
The question requires knowledge of contraindications for various vaccines, specifically in a child with a history of convulsions. This relates to the safety and adverse effects of vaccines, which is a crucial aspect of vaccine administration.

**Why the Correct Answer is Right**
In a child with a history of convulsions, the live, attenuated measles, mumps, and rubella (MMR) vaccine is contraindicated. This is because live vaccines contain weakened forms of the virus, which can potentially cause a more severe reaction in individuals with weakened immune systems or a history of seizures. The MMR vaccine can cause a reaction in a child with a history of convulsions, leading to further complications.

**Why Each Wrong Option is Incorrect**
* **Option A:** The inactivated poliovirus vaccine (IPV) is not contraindicated in children with a history of convulsions. IPV is a killed-virus vaccine, which cannot cause a live infection.
* **Option B:** The varicella vaccine, also a live, attenuated vaccine, may be contraindicated in children with severe immune suppression, but it is not specifically contraindicated in children with a history of convulsions.
* **Option C:** The conjugate pneumococcal vaccine is not contraindicated in children with a history of convulsions. This vaccine is made from polysaccharides, making it safe for use in individuals with weakened immune systems.

**Clinical Pearl / High-Yield Fact**
When administering vaccines to children with a history of seizures, it is essential to carefully evaluate the risks and benefits of each vaccine. Always consult the latest vaccine guidelines and consult with a pediatrician or infectious disease specialist if necessary.

**Correct Answer:** B.