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They replace Misbah-ul-Haq and Waqar Younis.
"The BCCI maintains that Test cricket is the ultimate format and we won't compromise it for anything," said Ganguly.
Raja, who played more than 250 international matches for Pakistan from 1984 to 1997, replaces Ehsan Mani who stepped down from his role last month.
There are reports doing the rounds that Kohli might lose his white-ball captaincy and Rohit Sharma could be asked to lead the limited-overs side if the team fails to win the ICC T20 World Cup.
It may depend on whether the various broadcasters, who paid 25 million pounds for the rights to the Old Trafford Test, would be willing to settle for two evenings' cricket rather than five full days.
The BCCI chief denied that the upcoming Indian Premier League had played any part in the cancellation of the final Test between England and India.
The Times of India reported that Rohit Sharma will take over as Indian captain in the shorter formats.
Instead of talking about the fifth Test being called off, Shastri chose to focus on the performances of the Indian team in the series.
Several cricket commentators, mostly British, have said that the cancellation had to do with the IPL and the huge money involved in the tournament.
If the ICC rules the Test as abandoned, then India will win the series 2-1 but if England get a forfeiture as per the DRC ruling, it will be a 2-2 verdict and the host nation can also claim insurance.
Results 5011-5020 of 5990