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Option 1: Guru Nanak Dev Ji - This option is incorrect. Guru Nanak Dev Ji was the founder of Sikhism and did not give the slogan `Back to the Vedas`.
Option 2: Dayanand Saraswati - This is the correct answer. Dayanand Saraswati, an Indian philosopher and social reformer, gave the slogan `Back to the Vedas`. He founded the Arya Samaj and advocated for the revival of Vedic principles and traditions.
Option 3: Swami Vivekananda - This option is incorrect. Swami Vivekananda was a disciple of Ramakrishna Paramahamsa and focused on the message of Vedanta and its practical application.
Option 4: Rajaram Mohan Roy - This option is incorrect. Rajaram Mohan Roy was a social reformer who championed various causes, but did not give the slogan `Back to the Vedas`.
In conclusion, option 2, Dayanand Saraswati, is the correct answer as he gave the slogan `Back to the Vedas`.