Find the number of zeros in the product:
1^1*2*2*3^3*4^4............98^98*99^99*100^100
A)1200
B)1300
C)1050
D)None of these

• B) 1300
  Number of zeroes will depend on number of multiplication by 10 in the given expression
  Also, 10=2*5
  Obviously there will be more 2's than 5's in the expression
  So we have to only fint the number of 5 in the given expression which if given by the numbers whose last digit it either 0 or 5:
  like 5^5 contains 5 '5's
  10^10 contains 10 '5's
  
  hence:
  5^5 - 05
  10^10 - 10
  15^15 - 15
  20^20 - 20
  25^25 - 2*25=50 (as 25=5*5 contains two 5's)
  30^30 - 30
  35^35 - 35
  40^40 - 40
  45^45 - 45
  50^50 - 100 (50=5*5*2)
  55^55 - 55
  60^60 - 60
  65^65 - 65
  70^70 - 70
  75^75 - 150 (75=5*5*3)
  80^80 - 80
  85^85 - 85
  90^90 - 90
  95^95 - 95
  100^100 - 200 (100=5*5*4)
  Hence total number of 5's= 5+10+15+20+50+30+35+40+45+100+55+60+65+70+150+80+85+90+95+200=1300
• 11 years agoHelpfull: Yes(38) No(1)
• calculate powers of 5 & multiple of 5...
  5+10+15+.......+100= 1050
  since in 25,50,75&100 contains 5^2
  so their respective powers should be added one more time
  25+50+75+100=250
  total=1050+250=1300 ans.
• 11 years agoHelpfull: Yes(28) No(1)
• is ter anyone here who can help me out in elitmus test i've my test on this sunday... 7th of july...
• 11 years agoHelpfull: Yes(7) No(0)
• the answer 1300 seems to be correct.If so, the answer given in book arun sharma i.e. 1050 is wrong
• 11 years agoHelpfull: Yes(4) No(0)
• me too friends aravind.mitra6@gmail.com send me all types of meterial u have abt Elitmus Questions
• 11 years agoHelpfull: Yes(1) No(0)
• the answer 1300 is correct and the answer given in arun sharma is also 1300
• 11 years agoHelpfull: Yes(1) No(0)
• the smallest no. that contains 0 is 10
  10=5*2 so just calculate no of 5 in the given expression
  the no that contain 5 are {5,10,15,20......}
  so taking this no only we have 5^5*10^10*.....100^100= ( 5^5*5^10*5^15....)=5^1050
• 11 years agoHelpfull: Yes(0) No(3)
• The answer is 1050
• 11 years agoHelpfull: Yes(0) No(3)
• mr.sumit pls expln d answer?
• 11 years agoHelpfull: Yes(0) No(2)
• I m having elitmus exam on nxt sunday...plz mail me all questions at shwetashrm.991@gmail.com
• 11 years agoHelpfull: Yes(0) No(0)
• plz mail me elitmus question or any study material to my email i:rahul260191@gmail.com.
• 11 years agoHelpfull: Yes(0) No(0)
• I m having elitmus exam on nxt sunday...plz mail me all questions and any study material at neetigupta.bu@gmail.com............plz plz its urgent........
• 11 years agoHelpfull: Yes(0) No(0)
• @arpit pls explain me the details abt '25^25'-50 ...pls pls...
• 11 years agoHelpfull: Yes(0) No(1)
• Answer will be 1050..
  since we need to count only nos of 5
  so count no. of 5 is 5^5+10^10+15^15+20^20.....100^100
  that will be 5+10+15+20+25+30......100 = 1050
• 11 years agoHelpfull: Yes(0) No(6)