Step 1: Concept
In $\beta^+$ decay (positron emission), a proton converts into a neutron, releasing a positron and a specific neutral particle to conserve lepton number.
Step 2: Meaning
$\beta^+$ is a positron ($e^+$). To balance the lepton number (which is 0 initially), the emission of a positron (lepton number $-1$) must be accompanied by a neutrino (lepton number $+1$).
Step 3: Analysis
If the decay was $\beta^-$ (electron), an anti-neutrino would be emitted. Since this is positron ($\beta^+$) emission from Carbon-11 to Boron-11, the accompanying particle is a neutrino ($\nu$).
Step 4: Conclusion
The particle 'X' is a neutrino.
Final Answer: (B)