The species that does not have unpaired electrons is:
 

1. \(N^+_2\) 2. \(O_2\)
3. \(O^{2-}_2\) 4. \(B_2\)
HINT: MOT diagram will tell about unpaired electron.
Explanation:
Step 1:
Draw the MOT diagram of the given species and find the number of unpaired electrons.
The electronic configuration of the given molecules are :
1.) N2+ =σ1s2, σ1s2*, σ2s2, σ2s2*, π2px2π2py2, σ2pz1
It has one unpaired electron.
2.) O2 =σ1s2, σ1s2*, σ2s2, σ2s2*, σ2pz2,π2px2π2py2, π2px1*π2py1*
O2 has two unpaired electrons.
3.)  O22- =σ1s2, σ1s2*, σ2s2, σ2s2*, σ2pz2,π2px2π2py2, π2px2*π2py2* 
Thus, O22- has no unpaired electrons.
4.) B2=σ1s2, σ1s2*, σ2s2, σ2s2*, π2px1π2py1
Thus, B2 has two unpaired electrons.
Step 2:
O22- ion does not contain unpaired electrons.