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The correct answer is option 1, Indira Gandhi.
An explanation for each option is as follows:
Option 1: Indira Gandhi - She is the correct answer as she never had to seek a trust vote from the Lok Sabha during her tenure as Prime Minister of India. This may be due to her strong majority in the parliament or other political factors.
Option 2: P.V. Narasimha Rao - Although P.V. Narasimha Rao served as the Prime Minister of India, he had to seek a trust vote in 1993 after his government faced allegations of bribery and corruption. Therefore, this option is incorrect.
Option 3: H.D. Devegowda - H.D. Devegowda became the Prime Minister of India in 1996 but due to lack of majority, his government collapsed and he had to resign. Therefore, he did have to seek a trust vote in the Lok Sabha. Hence, this option is incorrect.
Option 4: Manmohan Singh - Manmohan Singh served as the Prime Minister of India from 2004 to 2014. During his tenure, he faced multiple trust votes in the Lok Sabha, including the controversial nuclear deal with the United States in 2008. Therefore