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Number of ways of selecting two integers 'a' and 'b' from the set{1,2,3,4,.....5n}, n€N so that a 4 -b 4 is divisible by5? A)17n 2 +5n/2 B)15n 2 -17n/2 C)17n 2 -5n/2 D)15n 2 +17n/2

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


 

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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