The du’as in this post are those asking Allah for forgiveness. They appear in the Quran in the context when Prophet Moses (Moosa) made those Du’as to Allah. They can be recited to ask forgiveness from Allah for various sins.
The verse below refers to the incident when Prophet Musa (peace be upon Him) went to speak to Allah at Mount Tur. While at the mount, Musa (peace be upon Him) asked to see Allah. In earlier scriptures it was reported that Allah said to Musa, “O Musa! No living soul sees Me, but will perish, and no solid but will be demolished. As the verse states, after learning his mistake about asking Allah to see Him, Prophet Musa (peace be upon Him) asked Allah for His forgiveness (after he recovered from becoming unconscious from the slight effects that the glimpse of Allah’s light cast on the nearby mountain.)
The underlined words in the verse below is a du’a that glorifies Allah and asks for His repentance.
“And when Musa (Moses) came at the time and place appointed by Us, and his Lord (Allah) spoke to him; he said: “O my Lord! Show me (Yourself), that I may look upon You.” Allah said: “You cannot see Me, but look upon the mountain; if it stands still in its place then you shall see Me.” So when his Lord appeared to the mountain, He made it collapse to dust, and Musa (Moses) fell down unconscious. Then when he recovered his senses he said: “Glory be to You, I turn to You in repentance and I am the first of the believers.” [Qur’aan, Surah Al-A’raaf, 7:143].
The next verse refers to the incident of the calf that the nation of Children of Israel had made during Prophet Musa’s and Prophet Harun’s (peace be upon them) time. This occurred after Prophet Musa (peace be upon Him) went for the appointed term with his Lord at Mount Tur and appointed his brother, Prophet Harun (peace be upon Him), on his people. Allah describes the misguidance of those who worshipped the calf that As-Samiri (the magician) had made for them from various ornaments. He made the shape of a calf with these ornaments and threw on it a handful of dust from the trace of the horse that the Angel Jibreel was riding. This made the calf to moo and this drove people to start worshipping it. When Prophet Musa (A.S.) returned from the mount and saw his people astray, he asked Allah for forgiveness for himself and his brother.
The underlined words in the following verse is a du’a that Prophet Musa (peace be upon Him) made for himself and for his brother for forgiveness and asking for His mercy.
“Musa (Moses) said: “O my Lord! Forgive me and my brother, and admit us into Your Mercy, for you are the Most Merciful of those who show mercy.” [Qur’aan, Surah Al-A’raaf, 7:151].
 Tafsir Ibn Kathir