So many interpolated stories had cropped in the Mahabharata and one among those interpolated stories is fight between Karna and Jarasandha, which was narrated in the Shanti Parva.
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This interpolated story starts with Yudhisthira, after the war, asking Sage Narada about Karna and latter explaining the exploits of Karna. In the Chapter 5 of Shanti parva, it was narrated as follows:
"Narada said, 'Hearing of the fame of Karna's might, the ruler of the Magadhas, king Jarasandha, challenged him to a single combat. Both conversant with the celestial weapons, a fierce battle took place between them in which they struck each other with diverse kinds of arms. At last when their arrows were exhausted and bows and swords were broken and they both became carless, they began, possessed of might as they were, to fight with bare arms.
While engaged with him in mortal combat with bare arms, Karna was about to sever the two portions of his antagonist's body that had been united together by Jara.
The king (of Magadha), then after feeling himself very much pained, cast off all desire of hostility and addressed Karna, saying, 'I am gratified.' From friendship he then gave unto Karna the town Malini.
Before this, that tiger among men and subjugator of all foes (viz., Karna) had been king of the Angas only, but from that time the grinder of hostile forces began to rule over Champa also, agreeably to the wishes of Duryodhana, as thou knowest.
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Whenever we have a doubt, as to the authenticity of any incident in the EPIC, we have to cross check mention of that incident in other chapters of the EPIC.
a) The Shanti Parva and Anushasana parvas are interpolated in toto
The entire Shanti Parva and Anushasana Parva were narrated in a dialogue format, Yudhisthira being the listener and Bhishma, lying on the bed of arrows, being the narrator.
The issue involved here is that Bhishma had died on the 10th day of the war itself. The following is the narration of his death.
एवं कुरूणां पतिते शृङ्गे भीष्मे महौजसि । पाण्डवाः सृञ्जयाश्चैव सिंहनादं प्रचक्रिरे ॥
तस्मिन्हते महासत्त्वे भरतानाममध्यमे । न किञ्चित्प्रत्यपद्यन्त पुत्रास्ते भरतर्षभ ॥
सेनयोरुभयोश्चापि गाङ्गेये विनिपातिते । संन्यस्य वीराः शस्त्राणि प्राध्यायन्त समन्ततः ॥
When that great warrior of the Kuru clan, Bhishma, fell, the Pandavas and the Srinjayas roared in triumph. When the mighty grandson of Ganga was brought down, your son, O strong one of Bharata's lineage, was at a loss. As the formidable son of Ganga lay dead, the brave warriors of both sides set down their weapons and began to ponder thoughtfully.
Someone added subsequent shlokas indicating that Bhishma waited till the arrival of Uttarayana, lying on the bed of arrows.
Thus, the question of Bhishma lying on the bed of arrows and narrating various Dharmas to Yudhisthira does not arise. Thus, Shanti Parva and Anushasana parvas are interpolated in toto.
Hence, the story of fight between Karna and Jarasandha is an interpolation.
b) Dhritarashtra does not mention fight between Karna and Jarasandha
Before arrival of Shri Krishna to Hastinapura in Udyoga parva, Dhritarashtra says, while acknowledging the strength of Bhima, that it was because of Bhishma’s prowess that Jarasandha could not subjugate Hastinapura.
He did not mention the fight between Karna and Jarasandha there.
Without doubt, O Sanjaya, afflicted by the fear of Bhimasena, my sons and their dependents and all the allied kings will fly in different directions.
It was this Bhima who, having entered of old, with Vasudeva's aid, the innermost apartments of Jarasandha, overthrew that king endued with great energy; that lord of Magadha, the mighty Jarasandha, having fully brought under his subjection the goddess Earth, oppressed her by his energy.
That the Kauravas in consequence of Bhishma's prowess, and the Andhakas and the Vrishnis in consequence of their policy, could not be subjugated by him was due only to their good fortune.
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Hence, the story of fight between Karna and Jarasandha is an interpolation.