In $ {[Co{(CN)_6}]^{4 - }}\,and\,{[Co{(CN)_6}]^{3 - }} $ :
A. one is paramagnetic
B. second is diamagnetic
C. one is diamagnetic and second is paramagnetic
D. both A and B

Hint: In order to answer this question, to know the given compounds are paramagnetic as well as diamagnetic, we should check the electronic configuration of both the given compounds. If there is one unpaired electron then it's paramagnetic and if there is no unpaired electron, then it is diamagnetic.

Complete answer:
As we know that,
 $ C{O^{ + 2}} $ ion is present in $ {[Co{(CN)_6}]^{4 - }} $ while $ C{O^{ + 3}} $ ion is present in $ \,{[Co{(CN)_6}]^{3 - }} $ .
The electronic configuration of $ C{O^{ + 2}} $ and $ C{O^{ + 3}} $ ions in the ground state. While in the excited state, and undergoing hybridisation, $ C{N^ - } $ being a strong field ligand forces the inner $ d\,electrons $ to pair up.
Due to this, $ C{O^{ + 2}} $ in $ {[Co{(CN)_6}]^{4 - }} $ has one unpaired electron (i.e..it is paramagnetic) whereas, $ C{O^{ + 3}} $ in $ \,{[Co{(CN)_6}]^{3 - }} $ has no unpaired electron (i.e., it is diamagnetic).
Hence, the correct option is (D).

Note:
The paramagnetic materials or substance gets weakly magnetized under the application of a magnetic field. The diamagnetic materials or substances oppose the magnetism under the applied magnetic field. Same direction as of the applied magnetic field.