The remainder of $$\frac{{{{39}^{97!}}}}{{40}}$$ is :
A. 39
B. 0
C. 1
D. 13
E. None of these
Answer: Option C
Solution(By Examveda Team)
Since, $$\frac{{{{\text{a}}^{\text{n}}}}}{{{\text{a}} + 1}}$$ gives remainder 1 when 'n' is even.Now since, 97! is an even number so remainder will be 1.
Note:-Factorial of any no. is even.
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Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
the ans option is "c"