The court of Justice Bela Trivedi deferred the hearing to October 6 on a request made by Patel's lawyer seeking more time to file the affidavit in response to the petition.
The court had on August 21 issued notices to respondents including Election Commission, Patel and BJP leaders Amit Shah and Smriti Irani, who were elected as Rajya Sabha members.
Rajput, who was a Congress MLA and had quit the party just ahead of the August 8 Rajya Sabha elections held for three seats, was fielded as a BJP candidate.
Rajput has contended that votes of two other Congress MLAs should also be discounted as they had also shown their ballot papers to unauthorised persons. If this happens, he will emerge a winner.
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Rajput's petition said that once the returning officer had used his discretion to accept the two votes as valid, the EC had "no power to issue any direction to the returning officer for accepting or rejecting any vote".
The EC had rejected the votes of former Congress MLAs Raghavji Patel and Bholabhai Gohel.
Congress's polling agent Shaktisinh Gohil had lodged a complaint before the counting began that these two MLAs showed their ballots to BJP representatives before putting them in the ballot box.
MLAs are not allowed to show their ballots to anybody other than the authorised polling agent of their own party, the Congress leader said.
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