Explanation:

Rahim Khan’s tomb was opened to the public after six years of restoration work — perhaps the largest conservation project ever undertaken for any monument of national importance in India.

• Abdul Rahim Khan-i-Khanan (1556 – 1627), popularly known as simply Rahim, was a poet who lived in India during the rule of Mughal emperor Akbar.
• Abdul Rahim was the son of Bairam Khan, Akbar's trusted guardian and mentor.
• He was one of the nine important ministers (dewan) in his court, also known as the Navaratnas.
• Rahim is known for his Hindi dohe (couplets) and his books on astrology.
• Apart from writing various dohas, Rahim translated Babar's memoirs, Baburnama from Chagatai language to Persian language.
• He had an excellent command over the Sanskrit language. In Sanskrit, he wrote two books on astrology, Khetakautukam and Dwatrimshadyogavali.
• The village of Khan Khana, which is named after him, is located in the Nawanshahr district of Punjab.

Tomb of Abdul Rahim Khan-I-Khana

• His tomb is situated near Humayun's Tomb, in New Delhi. It was built by him for his wife in 1598, and his body was placed in it in 1627.

Comparison with Taj Mahal

• Five decades before the Taj Mahal was built by Shah Jahan, it was Abdur Rahim Khan-e-Khanan who built a tomb in Delhi in memory of his wife Mah Banu. It was the first Mughal tomb built for a woman.
• After his death in 1627, Rahim was also buried beside his wife, just like Shah Jahan was in the Taj.

Hence option 1st is correct.