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siri dhani Grade:
        

Number of ways of selecting two integers 'a' and 'b' from the set{1,2,3,4,.....5n}, n€N so that a4-b4 is divisible by5?


A)17n2+5n/2    B)15n2-17n/2    C)17n2-5n/2    D)15n2+17n/2


 

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear siri


give set {1,2,3,4,.....5n}


case 1:  when intiger a,b, are prime to 5.  then  (a4-1)  and (b4-1)  will be divisible by 5


  a4  -b=(a4-1)- (b4 -1) 


 total number of selecting rhe a,b  = 4n(4n-1)/2




case 2 : when a,b are  multiple of 5 


 total number of selecting rhe a,b  = n(n-1)/2




so total = 4n(4n-1)/2  + n(n-1)/2


               =17n2-5n/2


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Badiuddin

7 years ago
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