A N DIGIT NO HAVE THE FIRST AND LAST DIGIT SAME AND THE DIGIT IN BETWEEN ARE SAME ABBBBBBBBB....BA A AND B CAN NOT BE 0 AND A NOT EQUAL TO B FIND THE PROBABILITY THAT THE NO WILL DIVISIBLE BY 11

A- 1/2+3/72
b- 1/2+5/72
c- 1/2+8/72
d- 1/2+15/72

• ABBBBBB.....BA. let there r n B in bwn 2 A so total no of A and B will be.(2+n) if no. of B,s in bwn even then this no. will always will be devisible by 11.
  eg. 1221, 25555552,.....
  so either no. of B'S CAN BE EVEN or odd so prob will be 1/2.
  now if the n. of B'S are odd lets (2n+1)B.
  according to the divisibilty rule of 11 the sum of no.s at even places- the sum of no.at odd places shouldd be either 0 or should be divisible by 11.
  so,(2A+nB)-(n+1)B=2A-B= 0 or 11.
  for 0 there are four pairs (A,B).
  (1,2),(2,4),(3,6),(4,8).
  now for 2A-B = 11.
  (6,1),(7,3),(8,5),(9,7).
  so there are total 8 pairs of A & B.
  since A can have 9 values from 1 to 9 (becoz A cannot be zero.) then B can have 8 values ( because A nd B cannot be equal).so total posiible pair of A nd B are 72.
  so probabilty in secnd case will be 8/72.
  so total probability will be (1/2+8/72).
  so ans will be c.
• 10 years agoHelpfull: Yes(26) No(1)
• @vikas ---bha ur answer is perfect but what abour this
  if the no have odd digit
  then probaility must be 1/2*8/72
  why dont u mentioning the probsbilty of no being odd ie 1/2.
• 10 years agoHelpfull: Yes(0) No(3)
• was running. because she is exhausted now.
  it could have been "has been running" if some time was given
• 10 years agoHelpfull: Yes(0) No(7)
• nice sol @vikas
• 9 years agoHelpfull: Yes(0) No(0)