KEAM 2018 Math Paper

We know that, 54=625=13×48+1
⇒54=13λ+1, where λ is a positive integer.
⇒(54)24=(13λ+1)24
(by binomial theorem)
=(a multiple of 13)+1
On multiplying both sides by 5, we get
597=596⋅5=5( a multiple of 13)+5
Hence, the required remainder is 5