Wohooo... the same question was asked in our boards exam, this year !!!
ya exactly.. basic solution too have H ions... and after that its basic in nature coz of concentration !!!
actually.. in bases the concentration of H+ ions r low... nd this causes basicity !!!

Introduction:
Basic solutions are those which have a pH value greater than 7. These solutions contain hydroxide ions (OH-) instead of hydrogen ions (H+), which makes them basic. However, basic solutions may also contain a small amount of H+ ions.

Presence of H+ ions in basic solutions:
Basic solutions may contain a small amount of H+ ions due to the autoionization of water. In pure water, a small fraction of water molecules break apart into H+ and OH- ions. This is known as the self-ionization of water, and the concentration of H+ and OH- ions in pure water is equal (10^-7 M). In basic solutions, the concentration of OH- ions is higher than that of H+ ions, but there are still some H+ ions present due to the self-ionization of water.

Why are basic solutions basic?
Basic solutions are basic due to the presence of hydroxide ions (OH-) which have a strong affinity for H+ ions. When OH- ions come into contact with H+ ions, they combine to form water (H2O) molecules. This reaction reduces the concentration of H+ ions in the solution, which increases the pH value and makes the solution basic.

In addition, basic solutions may also contain other basic compounds such as metal hydroxides (e.g. NaOH) or organic bases (e.g. ammonia). These compounds also contain hydroxide ions which contribute to the basic nature of the solution.

Conclusion:
In conclusion, basic solutions may contain a small amount of H+ ions due to the self-ionization of water. However, the presence of hydroxide ions (OH-) in these solutions makes them basic. When OH- ions react with H+ ions, they combine to form water molecules which reduce the concentration of H+ ions and increase the pH value of the solution.