Which type of radioactive particle was emitted by the following isotopes?

Radioactive decay or disintegration is a process through which unstable nuclei form q more stable nuclei by the release of elementary particles like alpha particles, beta, protons, neutrons etc along with the release of energy.

In the given examples:

a) N-13 will get converted in to carbon, C-12 along with the release of a proton as shown below:

₇N¹³ →  ₆C¹²  +  ₁H¹

b) N-15 will get converted in to boron B-11 along with the release of an alpha particle

₇N¹⁵  →  ₅B¹¹  +  ₂He⁴

the answer to your question is c