According to Gnevyshev-Ohl (G-O) rule an odd-numbered cycle is stronger than its preceding even-numbered cycle. In the modern time the cycle pair (22, 23) violated this rule. By using the combined Greenwich Photoheliographic Results (GPR) and Solar Optical Observing Network (SOON) sunspot group data during the period 1874-2015, and Debrecen Photoheliographic Data (DPD) of sunspot groups during the period 1974-2015, here we have found that the solar cycle pair (22, 23) violated the G-O rule because, besides during cycle 23 a large deficiency of small sunspot groups in both the northern and the southern hemispheres, during cycle 22 a large abundance of small sunspot groups in the southern hemisphere. In the case of large and small sunspot groups the cycle pair (22, 23) violated the G-O rule in the northern and southern hemispheres, respectively, suggesting the north-south asymmetry in solar activity has a significant contribution in the violation of G-O rule. The amplitude of solar cycle 24 is smaller than that of solar cycle 23. However, Coronal Mass Ejections (CMEs) rate in the rising phases of the cycles 23 and 24 are almost same (even slightly large in cycle 24). From both the SOON and the DPD sunspot group data here we have also found that on the average the ratio of the number (counts) of large sunspot groups to the number of small sunspot groups is larger in the rising phase of cycle 24 than that in the corresponding phase of cycle 23. We suggest this could be a potential reason for the aforesaid discrepancy in the CME rates during the rising phases of cycles 23 and 24. These results have significant implication on solar cycle mechanism

9 pages, 9 figures, accepted for publication in Astrophysics and Space Science