Latest TCS Aptitude Question SOLUTION: no.of zeros in 1*2^2*3^3*....49^49

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(#M40033875) TCS Numerical Ability question no.of zeros Keep an EYE

no.of zeros in 1*2^2*3^3*....49^49

Asked In TCS santhoshi (11 years ago)

Solved RAKESH Read Solution (6)

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Read Solution (6) :

RAKESH  (11 years ago)

count the number of 5's

5^5 => 5 5's
10^10 = 2^10*5^10 => 10 5's
15^15 => 15 5's
20^20 => 20 5's
25^25 =(5^2)^25 = 5^50 => 50 5's
30^30 => 30 5's
35^35 => 35 5's
40^40 => 40 5's
45^45 -> 45 5's

total no. of 5's = 5 + 10 + 15 + 20 + 50 + 30 + 35 + 40 + 45 = 250

i.e. product has a term 5^250 , also no. of 2's is much more than 250

no.of zeros in 1*2^2*3^3*....49^49 = 250

Is this solution Helpfull? Yes (22) | No (4)  

Shruti  (10 years ago)

ans is 250.

Is this solution Helpfull? Yes (3) | No (3)  

prabhakar kumar  (11 years ago)

0,it does not consist any zero.

Is this solution Helpfull? Yes (1) | No (12)  

Aakash Jain  (11 years ago)

no. of zero =20
1*2^2*3^3.....49^49=(49!)^2
and no of zero in 49! is =no. of 5's
no. of 5 in 49! =49/5+49/5^2+....
total no of 5 in 49!=10
and no of 0's in (49!)^2=10*2=20

Is this solution Helpfull? Yes (1) | No (3)  

Asmita Raha  (11 years ago)

Answer will be 250

Is this solution Helpfull? Yes | No (1)  

rupak ghosh  (11 years ago)

105..
5^5 has one 5 with which any even no will multiply to give one 0,so for 1,25,35,45...so total five 0's.and 10^10,20^20,30^30,40^40 gives 10+20+30+40=100 0's.They will multiply to produce 105 no of 0's.

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