Ques:- What are your long term professional goals?
Ques:- Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeros will the product end?
A. 1
B. 4
C. 5
D. 10
Recent Answer : Added by Yash G On 2023-03-01 17:24:09:
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
Ques:- Document sorting
Ques:- A/B = 3/5 15A = ?
Recent Answer : Added by Admin On 2020-05-17 11:59:28:
5A=3B,
*3 SO,
15A=9B
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Ques:- A can copy 50 papers in 10 hours while both A & B can copy 70 papers in 10 hours. Then for how many hours required for B to copy 26 papers?
Recent Answer : Added by Admin On 2020-05-17 12:04:30:
A can copy 50 papers in 10 hrs
that means 5 papers in 1 hour
A & B can copy 70 papers in 10 hrs
that means both of them copy 7 papers in 1hour
we know A can copy 5 papers
there fore B can copy 2papers in 1 hour
so B can copu 26 papers in x hours
2*x=26
x=26/2=13 hours
Ques:- Why want to leave
Ques:- You are given 8 identical balls …. but one of them is slightly heavier than the rest…. given a old scale (not electronic one) and only two trials to weigh … can u spot the odd one out????
Ques:- 50% of 250 is what % of 300?
Recent Answer : Added by Nanthini A On 2021-09-07 16:10:18:
60%
Ques:- The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Recent Answer : Added by SHWETA On 2021-11-26 16:30:43:
4500 sal of jan
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Ques:- The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Ques:- In each questions below are given two statements followed by two conclusions numbered I and II. Statements : Most teachers are boys. Some boys are students. Conclusions :
I. Some students are boys. II. Some teachers are students.
A. if only conclusion I follows
B. if only conclusion II follows
C. if either conclusion I or II follows
D. if neither conclusion I nor II follows
E. if both conclusions I and II follow
Ques:- What’s your dream job?
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Ques:- 0,7,26,63,124, ?
Recent Answer : Added by apticracker On 2022-09-02 17:04:47:
Ques:- There are 4 people in a closed room and you are waiting outside to enter into the room. You can enter only when one of them opens the door. The probability that somebody will open the door is 1/2. Now what is the probability that the door will be opened so that you can go inside?
Recent Answer : Added by Ashwin GB On 2021-07-08 16:28:54:
The probability that no one opens the door would be
0.5×0.5×0.5×0.5= 0.0625
So, the probability that atleast one opens the door is 1-0.0625= 0.9375
Ques:- What is your main role in last company & work process?
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Ques:- A bus started from the bus stand at 8 Am and after staying 30 minutes at a destination return back to the bus stand. The Destination is 27 miles from the bus stand . The Speed of the bus is 18mph . In the return journey the bus travells with 50% fast speed.At what time it is return to the bus stand ?
Recent Answer : Added by Admin On 2020-05-17 12:00:34:
Bus started at 8:00
it travelled with 18mph…
distance of destination is 27 miles…
we know velocity=(distance)/time
i.e., time=27/18hours=3/2hours=90 min…
i.e., the bus reached destination at 9:30
the bus stayed for 30 min…
so the bus started return journey at 10:00
now the bus returned with velocity 18 + (18/2)=27mph
the taken to the bus to travel = 27/27=1 hour = 60 min…
so bus would be returned on 11:00…
Ques:- Find out the wrong number in the series: 40960, 10240, 2560, 640, 200, 40, 10
A. 40
B. 200
C. 640
D. 2560
Recent Answer : Added by Mahendra Sharma On 2022-08-14 16:41:55:
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