Cross-sections for production of evaporation residues from the compound nucleus⁹⁶Ru* formed by fusion reactions²⁸Si+⁶⁸Zn,³²S+⁶⁴Ni,³⁷Cl+⁵⁹Co and⁴⁵Sc+⁵¹V have been obtained from the yields of their characteristicγ-rays. The measurements span an excitation energy range of 55 MeV to 70 MeV of the compound nucleus. The evaporation residue (ER) cross-sections have been analysed in terms of statistical model for the decay of the compound nucleus. A good agreement is found between statistical model calculation and the experimental evaporation residue cross-sections in all the four cases. It is shown that the average angular momentum$$\bar \ell $$ of the compound nucleus can be deduced from a comparison of the experimentally measured and the statistical model predictions for the ER cross-sections. The validity of this method of deriving$$\bar \ell $$ has been discussed for the case of¹⁶O+¹⁵⁴Sm system.