"For us there are scary memories of Gujarat and Godhra riots. As the prime minister of India, Modi will have to prove he was not behind those events," said Muzaffar Ahmad, a college teacher.
"For this to be done and seen, Kashmiri Muslims and others living outside will have to be taken on board through positive action.
"He cannot rule without being every Indian's prime minister. Winning elections is one thing but governing a vast, multi-religious, multi-ethnic, multi-cultural country like India is a very difficult call," he added.
According to Ahmad, "the most difficult task would be working for better ties with Pakistan and winning the hearts and minds of Kashmiris".
Added Noor Muhammad Wani, 61, a resident of Shalteng in Srinagar's outskirts: "Congress failure or deliberate reluctance to resolve the Kashmir dispute somehow gives me an impression that Modi will definitely ensure peace in Kashmir. This will be possible only if he takes Nawaz Sharif on board."