Statement - I : Systametic errors are due to a definite cause and can be minimised.
Statement - II  Random errors are due to unknown reasons and can be completely eliminated.

Systematic errors can be minimised by improving experimental techniques, selecting better instruments and removing personal bias as far as possible. For a given set up, these errors may be estimated to a certain extent and the necessary corrections may be applied to the readings. Hence 1 is correct.
Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions.

Systematic error can be eliminated to a sufficient degree, whereas random error cannot.so 2 is wrong.