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Number Theory Related Questions by Balaji
#1


(55555.......2013 times ) divided by 440, what is the remainder ?

a) 5



b) 155



c) 115



d) 125


answer choice c

solution


N/8 remainder =3
N/5 remainder =0


N=8k+3


N can take -27,115,203,291,379


N=440c + 115


 




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#2

The product of two non-coprime number is 1080. how many such pairs are possibles ?



a) 16



b) 4



c) 12



d) 15



answer choice c

solution


a*b=1080
no of factors =4*4*2=32

no of ways of writing 1080 as a product of two non coprime no = 16-4=12
 




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#3


(234)n


(1ab)n/(b21)n


find (a+b)

a) 11



b) 8



c) 7 or 11



d) 9



answer choice d



solution



4+b=n+1

where b=4

8=n+1

n=7

4+a=n+2

4+a=9

a=5

a+b=9


 




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