Yes,it is permissible though it is not recommended.

Can a person read the quran (hard copy) lying down?

Reading/Reciting the Quran | March 12, 2014 12:18 pm
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Can you please state some of the benefits of reading the following Soorahs with references to Hadith. Soorah Naba , Soorah Al-Waqiah , Soorah Yaseen , Soorah Mulk?
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Is it mandatory for women to cover their head for reading the HOLY QURAN?