Concept:
A positron is the antiparticle of an electron. It has
\[
\text{charge}=+e,
\]
and is emitted during \(\beta^+\)-decay.
Step 1: Recall the process of \(\beta^+\)-decay.
In \(\beta^+\)-decay, a proton inside the nucleus transforms into a neutron.
\[
p
\rightarrow
n+e^+ + \nu_e,
\]
where
\[
e^+ = \text{positron},
\]
\[
\nu_e = \text{neutrino}.
\]
Step 2: Examine the other decay modes.
\[
\alpha\text{-decay}
\]
emits a helium nucleus
\[
{}^{4}_{2}\mathrm{He}.
\]
\[
\beta^-\text{-decay}
\]
emits an electron.
\[
n
\rightarrow
p+e^-+\bar{\nu}_e.
\]
\[
\gamma\text{-decay}
\]
emits electromagnetic radiation (gamma photons).
None of these emit positrons.
Step 3: Identify the correct decay.
Only
\[
\boxed{\beta^+\text{-decay}}
\]
involves the emission of a positron.
Therefore,
\[
\boxed{\text{Answer = (B)}}
\]