Ques:- How many mashes are there in 1 squrare meter of wire gauge if each meshis 8mm long and 5mm wide ?(a) 2500(b) 25000(c) 250(d) 250000
Recent Answer : Added by Nathan Abebe On 2022-04-02 06:59:54:
B, 8mm x 5 mm = 40 mm^2
1000mm x 1000mm = 1,000,000mm^2
= 1,000,000 mm^2/40mm^2
= 25,000
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Ques:- A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
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
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Recent Answer : Added by Admin On 2020-05-17 11:59:43:
66 seconds
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A. Krishna
B. Tapti
C. Narmada
D. Chambal
Recent Answer : Added by Azeem On 2021-09-25 16:19:47:
Chambal
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8925
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Recent Answer : Added by Admin On 2020-05-17 12:04:18:
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63:45:55
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A. 22
B. 24
C. 44
D. 48
Recent Answer : Added by narendra On 2022-09-18 09:02:11:
c
Ques:- Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)
Recent Answer : Added by Admin On 2020-05-17 12:01:52:
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Ques:- Pipes P and Q can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
B, 8mm x 5 mm = 40 mm^2
1000mm x 1000mm = 1,000,000mm^2
= 1,000,000 mm^2/40mm^2
= 25,000