Over the 120 y period (1871--1990) for which reliable Indian rainfall statistics are available, solar activity parameters exhibit nonstationarity. Taking this fact into account, we present here the results of an analysis of four solar activity indices and seven major Indian monsoon rainfall time series, over two distinct test periods respectively of low and high solar activity, each comprising three complete solar cycles. It is found that the average rainfall is higher in all seven rainfall indices during periods of greater solar activity, at confidence levels varying from 75% to 99%, being 95% or greater in three of them. Using wavelet techniques it is also found that the power in the 8--16 y band during the period of higher solar activity is higher in 6 of the 7 rainfall time series, at confidence levels exceeding 99.99%. These results support existence of connections between Indian rainfall and solar activity.