Step 1: Understanding the Question:
The goal is to determine the individual oxidation states of Carbon (C) and Hydrogen (H) in a neutral molecule of methane ($CH_4$).
Step 2: Key Rules or Approach:
The following standard rules for assigning oxidation states are applied:
1. The oxidation state of Hydrogen is $+1$ when it is bonded to non-metals (Carbon is a non-metal).
2. For any neutral molecule, the algebraic sum of the oxidation states of all its constituent atoms must be zero.
Step 3: Detailed Explanation:
Let the unknown oxidation state of Carbon be represented as $x$.
Methane ($CH_4$) consists of one Carbon atom and four Hydrogen atoms.
As per the rules, each Hydrogen atom is assigned an oxidation state of $+1$.
Applying the rule for the sum of oxidation states in a neutral molecule:
\[ 1 \times (\text{Oxidation state of } C) + 4 \times (\text{Oxidation state of } H) = 0 \]
Substituting the assigned value for Hydrogen:
\[ x + 4 \times (+1) = 0 \]
\[ x + 4 = 0 \]
\[ x = -4 \]
This calculation confirms that Carbon has an oxidation state of $-4$ and each Hydrogen atom has an oxidation state of $+1$.
Step 4: Final Answer:
The oxidation states of C and H in $CH_4$ are $-4$ and $+1$ respectively, which corresponds to option (B).