find remainder of (9+9^1+9^2+.........+9^n)/6
n is multiple of 11.
a) 2
b) 5
c) 3
d) 0

• 9 div 6=3 rem
  
  3*11=33
  33/6 =3 rem
  
  3*22=66
  66/6= 0rem
  
  99/6= 3 rem
  
  so 3 and 0 ill be rem( when even no. comes rem ill be 0 else 3)
  
• 7 years agoHelpfull: Yes(19) No(5)
• 1-IF YOU WILL TAKE COMMON 9 FROM THE EXPRESSION , IT WILL BE
  9{1+1+9+9^2+....9^(N-1)}
  2-IF WE WILL DIVIDE 6 FROM THE ABOVE EXPRESSION IT WILL GIVE 3 AS REMINDER .
  9/6, REM = 3
  3- 3 WILL BE THE ANSWER .
  *DOESNT DEPEND ON VALUE OF N
• 7 years agoHelpfull: Yes(11) No(6)
• remainder will be 3
  as no matter what power of 9 is...if it is divided by 6 , the remainder will be 3 only
• 7 years agoHelpfull: Yes(7) No(9)
• answer will be 3. because sum of power of 9 upto even powers is divisible by 6
  and upto odd powers it will give the remainder 3 everytime
  
• 7 years agoHelpfull: Yes(2) No(0)
• everyone is wrong here.
  correct answer is 5.
  
  9^1/6 = 3
  9^2/6 = 1
  likewise 9^odd/6 = 3
  9^even/6 = 1
  
  3*6+ 1*5 = 23/6 = rem = 5
• 7 years agoHelpfull: Yes(2) No(4)
• =9/6+(9^1+9^2+....9^11*n)/6
  =9/6+3/6
  then =12/6=0
• 7 years agoHelpfull: Yes(1) No(3)
• It can be both 3 and 0 . If n=11 then its (9+ 3*11) /6 gives 0 remainder if n=22 then it becomes ( 9+ 3*22)/6 gives 3 as remainder
• 7 years agoHelpfull: Yes(1) No(0)
• Taking n as 11 and proceeding further, step wise
  9^11 = 31381059609
  9^10 = 3486784401
  9^9 = 387420489
  9^8 = 43046721
  9^7 = 4782969
  9^6 = 531441
  9^5 = 59049
  9^4 = 6561
  9^3 = 729
  9^2= 81
  9^1 = 9
  + 9
  -------------------
  35303692063
  --------------------
  
  Now dividing these number by 6 we get remainder as 5.
  
  So, the correct answe is b) 5
• 7 years agoHelpfull: Yes(1) No(7)
• correct answer is 3.
  
• 7 years agoHelpfull: Yes(1) No(1)
• for odd multiples of 11 the answer is 3 and for even multiples of 11 ans is 0 so here the answer as per question is cant be determined as we dont know whether the power is even or odd multiple
• 7 years agoHelpfull: Yes(0) No(0)
• in 1 to 10 the odd no is 5
  11 to 20 odd no. is 5
  similarly 90 to 100 odd no is 5
  so total no. is up to 100 is 50
  so 50 *100=5000
• 7 years agoHelpfull: Yes(0) No(1)
• can not be determined bcz here 11 is multiple .because here we can take the value of n is even or odd .
• 7 years agoHelpfull: Yes(0) No(1)
• Use calculator Ans will be 3
• 7 years agoHelpfull: Yes(0) No(0)
• 9+9^1+9^2...........+9^n=9+9(9^11-1)/9-1 formula to sum of gp series
  
  9+9(9^11-1)/9-1 =9(1+9^11-1)/8
  
  9*9^11/8
  
  now we r taking 6 the is given in the question
  =9*9^11/6*8
  =3*9^11/16
  =27*9^10/16
  27/16=11 rem
  9^10/16=10 rem
  11+10=21/16=5
  
  
  5 will be the answer
• 6 years agoHelpfull: Yes(0) No(0)
• If we divide numerator and denominator by 3 then we will get only 2 in denominator... which means only 0,1 can be remainder... so i think 0 should be the answer.
• 4 years agoHelpfull: Yes(0) No(0)