To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.
The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.
There are 24 primes in S, so the product of S is:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.
5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.
25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.
Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros
17 secs
13 and 15
15 min 100 line
30 min 200 lines + 15 min rest total 45 min +5 min think +5 min write + 5 min rest
250 line code will be done
15%
MBA refers to Master Of Business application, so that the line says as well our day to day life is also consider as an business, and second by science stream but why not in other, it depends on the capacity of student and smart move kind off.
120
10, 14, 28, 32, 64, 68, 132
132
Answer is 10km
first fill 3quart pail and pour in 5quart pail.fill again 3
quart pail and fill remaining 2 quarts in 5 quart
pail.hence 1 quart remains in 3quart pail.empty 5quart pail
and pour 1 quart from 3 quart pail. also add another 3
quart from 3 quart pail. hence 1 + 3 quarts = 4 quarts.
3600 sec in 1 hr.. 1000 M in 1 km so to covert m/s to km /hr you multiply the value with (3000/1000) .. so 3000 divided by 1000 will give you 18/5 it’s like constant value.. to convert m/s to km/ hr we can use this 18/5.. hope you understand
10
Circular Track sis of 11 km
Speed of Mens are
4 , 5.5 , 8 km/hr
Time at Which they are at starting Points again
11/4 , 11/5 , 11/8
11/4 , 2.2 , 11/8
We need to find LCM of these
to find at what time they Meet again at starting point
LCM 11 * 2 = 22
After 22 Hrs they will meet at starting point
Solution # 15-18
Sitting solution be- D T M B H R
Ans 15 :Mr. D
ans 16 : 1 2 3
Ans 17 : 3
Ans 18 : Mr B Suffering from anemia.