50^51^52 /11
a)6
b)4
c)7
d)3
ans is 6 but expln in detail

• Ans 6
  We know that 6^1=6 or 6^2=36 so for all power of 6 unit digit is 6 now que is 50^51^52 now if we divide 50/11 then rem is 6 means 6^51=6 at unit place same for 6^52 salso give 6 at unit place now finally 50^51^52 gives 6 at unit place now 6/11=6 Ans
• 9 years agoHelpfull: Yes(18) No(3)
• Z=52 %4 =0; (1st divide by 4 and get rem.)
  Y=51 %10=1; (2nd divide by 10 and get rem.)
  
  b=Y^z= 1^0=1;
  a = b%10= 1% 10 =1; ( again divide by 10 and get rem. )
  
  lastly, 50^ a= 50^1/11 and get rem. = 6
  
• 9 years agoHelpfull: Yes(7) No(0)
• Remainder when 50^1 is divided by 11 -> 6
  Remainder when 50^2 is divided by 11 -> 3
  Remainder when 50^3 is divided by 11 -> 7
  Remainder when 50^4 is divided by 11 -> 9
  Remainder when 50^5 is divided by 11 -> (-1) BINGO!
  
  So that: Remainder when 50^10 is divided by 11 -> 1
  
  Conclusion:
  
  Remainder when 50^(10*x+y) is divided by 11 would be the same as that of when 50^y is divided by 11 that is we just need the last digit of the power of 50.
  
  And the last digit of 51^52 is 1.
  
  Remainder when 50^1 is 6.
  
  Finally 50^51^52 when divided by 11 gives a remainder of 6.
• 9 years agoHelpfull: Yes(4) No(4)
• We want 50^(51^52) mod 11.
  From simple application of Fermat's little theorem we know that
  50^10 = 1 (mod 11).
  
  Also we can say that 51^n = 1 (mod 10) where n is any positive integer.
  Therefore, 51^52 = 1 (mod 10) which implies 51^52 = 10*m + 1 for some positive integer m.
  So, 50^(51^52) = 50^(10*m+1) = 50. 50^(10*m)
  As we know 50^10 = 1 (mod 11) we can say that 50^(10*m) is also 1 (mod 11). So 50^(51^52) = 50^(10*m+1) = 50. 50^(10*m) = 50. 1 (mod 11).
  so 50 (mod 11) = 6
• 9 years agoHelpfull: Yes(3) No(3)
• On dividing first 50 by 11 we got 6 as remainder thus now we,are left with 6^51^52/11 our approach should be to simplify calculation so doing (6^5= 7676 /11 gives 1 remainder it simplifies calculation)
  ((6^5)^10 * 6)^52/11
  So,we have (1^10*6)^52/11
  (6^52)/11
  Now 52=4n form and we know in term of 6 4n,4n+1,4n+2,4n+3 all are 6 so 6/11=6 ans
• 9 years agoHelpfull: Yes(3) No(2)
• i think it is 3
  50%11=6 so 6^51^52
• 9 years agoHelpfull: Yes(2) No(5)
• ans is option A=6
• 9 years agoHelpfull: Yes(1) No(9)
• 50^51^52/11= 52/4 & 51/10 & 52/11=6^1^0/11=6 ans
• 9 years agoHelpfull: Yes(1) No(5)
• Its simple..50^51^52 mod11
  51^52=how to find last two digits .units place will be 1^2=1.tenths place will be 5*2=10. So comming 101..now 50^101.using same rule we get 0 in units place and 5 in tenths place . So 50/11.rem is 6
  
• 8 years agoHelpfull: Yes(1) No(0)
• plz give explanation so that everybody can understand the soultion
• 9 years agoHelpfull: Yes(0) No(1)
• use eulers rule to solve it eassly ans is 6
• 9 years agoHelpfull: Yes(0) No(0)