Arshad Shafique Ansari, Fahimida Sayyed, 37, and her daughter Fareen Sayeed, 17, appeared in the Special Court in Bombay on Monday.
They were remanded in police custody until 15 September.
The other accused, Sayyed Muhammed Abd al-Rahim, 45, husband of Fahimida Sayyed, did not appear in court as he was admitted to a hospital, prosecutor Rohini Salian said.
The four were detained under strict anti-terrorism laws that carry the death sentence.
Prosecutors said the accused were also involved in the 28 July bombing of a bus packed with commuters in Bombay, which killed four people and left 43 injured.
Police sources said the four had links with the Lashkar-e-Taiba group, which was fighting to force the Indians to withdraw from Kashmir.
Indian Prime Minister Atal Behari
They added they had close ties with the Students Islamic Movement of India (SIMI), which India banned last year after accusing it of fomenting sectarian trouble.
But the BBC reported Bombay residents as saying that they believed the arrested were locals with no ties to political groups.
Prosecutors said police seized 205 gelatine sticks, 20 detonators, 12 alarm clocks with timers, electric wires, and firecrackers from the accused.
The four accused were charged under the draconian Prevention of Terrorism Act (POTA).
The anti-terrorist law was passed by the ruling Bharatiya Janata Party (BJP) in 2002 in the face of nationwide political opposition.
Critics say it allows the government to hold suspects without charge for extended periods, and puts the burden of proof on the accused.