Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If 5 97 is divided by 52, then the remainder obtained is
Text Solution
Verified by ExpertsThe correct answer is:
B
5
We know that, 5 4 = 625 = 52 x 12 + 1
5 4 = 52 
+ 1 , where 
is a positive integer.
(5 4 ) 24 = (52 
+l) 24
= 24 C 0 (52 
) 24 + 24 C 1 (52 
) 23 + 24 C 2 (52 
) 22 + . .. + 24 C 23 (52 
) + 24 C 24 (by binomial theorem)
5 96 = 52 [ 24 C 0 52 23 
24 + 24 C 1 52 23 
22 + ... + 24 C 23 
] + 1
= (a multiple of 52) + 1
On multiplying both sides by 5 , we get
5 97 = 5 96 . 5 = 5 (a multiple of 52) + 5
Hence, the required remainder is 5 .
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