find the remainder when 32^33^34 is divided by 11 ?
a)5
b)10
c)4
d)1

• as i have explained earlier we can use remainder theorem when consecutive no. are there...so here we cosider it as 32*33*34 but as 33 divisible its not required so 32*34 so taking -ve and +ve remainder i.e. (-1)*(1) = -1 now the remainder is
  11-1 = 10.(bcoz when the remainder is -ve we subtract it from no. dividing) so ans is 10.
• 11 years agoHelpfull: Yes(82) No(30)
• 32^33=(-1)^33=(-1)
  and (-1)^34=1
  so ans is 1
• 11 years agoHelpfull: Yes(27) No(42)
• is there any method to solve these type of questions when powers are not consecutive.?
• 11 years agoHelpfull: Yes(15) No(10)
• 32^33^34 now 33^34 can be written in form (10k+9)(coz unit digit iz 9)
  so 32^(10k+9)/11..remainder=(-1)^(10k+9)=mod(-1)
  so remainder will be 10.
  ans b)10.
• 11 years agoHelpfull: Yes(12) No(22)
• 32/11 = 10
  32^2 /11 = 1
  32^3 /11 = 10
  
  33^34 is odd number
  when 32^(oddnumber) is divided by 11 remainder is 10
  
  
  Answer is 10
• 9 years agoHelpfull: Yes(6) No(0)
• @Mr.AVISEK- plz explain find the remainder when 33^34^35 divided by 7
• 11 years agoHelpfull: Yes(4) No(4)
• lets 32^33=32*32*32*....33th time.
  y=32^33^34=(32*32*32*....33th time.)*(32*32*32*....33th time.)........34times.
  so,y=32*something.
  y/11 remainder 10
  so finally remainder will 10.
  
• 9 years agoHelpfull: Yes(4) No(2)
• Look for the cycle..!
  33^34 is going to give an odd number since the unit digit will be 9...
  NOW,32^1 when divided by 11 gives remainder 10..
  32^2 when divided by 11 gives remainder 1..
  32^3 when divided by 11 gives remainder 10..
  So this means if 32^odd,we'll get remainder 10..!
• 9 years agoHelpfull: Yes(4) No(0)
• @vikas can u plz xplain y n where to use this kinda fundas??? :- {(10k+9)(coz unit digit iz 9)}
  and ny1 plz help me with the soln of 50^56^52 wen divided by 11 wil gv a remainder of?? n plz xplain in detail as m helpless in solving qns wid powerr based on remainder theorem.
• 11 years agoHelpfull: Yes(3) No(1)
• 10 is correct answer
• 11 years agoHelpfull: Yes(2) No(14)
• 10 z d right answer
• 11 years agoHelpfull: Yes(2) No(5)
• @SALONI SINGH
  for 50^56^52 /11 ans will be ...5
  
• 9 years agoHelpfull: Yes(2) No(0)
• 32^33=last two digits 92, then 92^34=last two digits 21, than 21/11=1-10/11
  so here remainder is 10
• 9 years agoHelpfull: Yes(0) No(0)
• If the question is R(32^33^34/11)=?
  
  32^33^34≡(33−1)^33^34≡(−1)^33^34≡(−1)≡(11−1)≡10
• 5 years agoHelpfull: Yes(0) No(0)
• answer is 10
• 5 years agoHelpfull: Yes(0) No(0)
• (32*32*......33 times)*(32*32*......33 times)*.........................*34 times
  32%11 is 10. (10*10)%11 is 1. so, in first (32*32*......33 times), 10 is remainder 33 times
  ==> 1 is remainder 12 times and 10 is remainder one time
  ==> 10 is remainder 1 time
  ==> 34 times the expression (32*32*......33 times) means 34 times 10
  ==> 17 times 1 i.e., 1*1*1..........17 times
  ==> the remainder will be 1
• 4 years agoHelpfull: Yes(0) No(0)