(Reuters) - Activity in China's services sector grew modestly in February as new orders rose at their quickest pace in three months, a private survey showed just a few days after the central bank cut interest rates to stimulate the world's second-largest economy.

The HSBC/Markit Services Purchasing Managers' Index(PMI) picked up to 52.0 last month from January's 51.8 and remained above the 50-point level that separates contraction from growth in activity on a monthly basis.

A sub-index for new orders rose to 52.2 in February from 51.2 in January and the sub-index measuring new business also rose.

Official surveys showed on Sunday that growth in the services sector picked up to 53.9 last month from January's 53.7, which the National Bureau of Statistics attributed in part to strong holiday spending during the Lunar New Year holidays.

China's economic growth slowed to 7.4 percent in 2014 - the weakest in 24 years, from 7.7 percent in 2013, even as the job-creating services sector outperformed the factory sector.

A further slowdown to around 7 percent is expected this year, even allowing for additional stimulus measures, as a cooling property market, excess manufacturing capacity and slowing investment weigh on activity.

(Reporting by Judy Hua and Pete Sweeney; Editing by Kim Coghill)