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In this scenario R0 is only providing backup to main links of R1, R2, R3. And it should only use in the failure of main links. This is a tricky question. Its directly related to administrative distance. As we know Administrative distance of RIP is120 and EIGRP is90. If both protocol exist on same router and have path for destination, EIGRP path will be chosen by default as it have low AD value. And in routing decision low AD value is winner.
