Why Yudhisthira went to hell?
Yudhishthir was taken to hell and had heard all his brothers, wife and sons screaming out of pain there but that was just an illusion created by the Gods only for a small amount of time so that he suffers a bit mentally and due to that his only sin of being untruthful at the time of Drona's killing, can be redeemed. According to Chapter 5 of Mahabharata's Swargarohanika Parva, following is what is told to Yudhishthir after he sees his brothers, wife, etc suffering in hell:
O son of Pritha, thy brothers, O king, were not such as to deserve Hell. All this has been an illusion created by the chief of the gods.
O king, that desirous of doing thee good, I caused thee to be sent for having a view of Hell. Thou hadst, by a pretence, deceived Drona in the matter of his son. Thou hast, in consequence thereof, been shown Hell by an act of deception. After the manner of thyself, Bhima and Arjuna, and Draupadi, have all been shown the place of sinners by an act of deception. Come, O chief of men, all of them have been cleansed of their sins. All those kings who had aided thee and who have been slain in battle, have all attained to Heaven.
Regarding Duryodhana, he has in heaven not because he has been untruthful, but because it is said that if a Kshatriya dies while fighting in a battle, he attains heaven because this is Kshatriya dharma. He died during battle performing his duties therefore he was ought to get heaven.
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