In [30]: df.dropna(subset=[1])   #Drop only if NaN in specific column (as asked in the question)
Out[30]:
          0         1         2
1  2.677677 -1.466923 -0.750366
2       NaN  0.798002 -0.906038
3  0.672201  0.964789       NaN
5 -1.250970  0.030561 -2.678622
6       NaN  1.036043       NaN
7  0.049896 -0.308003  0.823295
9 -0.310130  0.078891       NaN