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Comparing exponents and factorials

Source: LIMIT 2020 Cat 1 Obj P19

May 2, 2020
limitalgebrafactorial

Problem Statement

Let a=20191009,b=2019!a=2019^{1009}, b=2019! and c=10102019c=1010^{2019}, then which of the following is true?
(A)c<b<ac<b<a (B)a<b<ca<b<c (C)b<a<cb<a<c (D)b<c<ab<c<a
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