NEW DELHI—Google Inc. and Facebook Inc. are set to begin trial here Tuesday to face charges that they didn't censor objectionable content from their sites, putting on stark display the legal risks for Internet companies chasing growth in India.

The case is the highest-stakes example yet of the controversy in India over what role Internet companies should have in policing content on the Web. If convicted, executives from the companies could face jail time and the companies could face fines, lawyers following the case said.

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