This research is designed to study the weak form efficiency in the Indian stock Market. To keep the research design in-line with the research objectives the researcher has taken due care, that the tools used in research are objective oriented. Stock markets are full of wonders. Several times, they move without any logical reasons, while several times they do not react to some specific information in an expected manner. This kind of nature of markets is named as random walk theory or weak form efficiency by researchers. On the other hand, quite a few times, markets perform in the direction of expectations around some events. The research data are analyzed using descriptive and inferential statistics distribution patterns (test for normality of distribution of price changes), which is a measure of the randomness of price changes, serve as the descriptive statistics while inferential tests consist of testing the SENSEX and NIFTY of the Indian stock exchange for independence (using serial correlation test), randomness (using runs test, Variance Ratio test), stationarity (using Unit root test) and Volatility (using ARCH and GARCH models).