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Ques:- If 2x y = 10 and x = 3, what is x – y
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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Ques:- A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Recent Answer : Added by vinita On 2022-08-14 16:33:16:
4 mins
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Ques:- In a certain company 20% of the men and 40% of the women attended the annual company picnic. If 35% of all the employees are men .What % of all the employee went to the picnic?
Recent Answer : Added by Admin On 2022-09-29 17:55:57:
Suppose that total 100 employees are in company….. out of that 35 are man and remaining 65 are women.
20% of man 35 = 20*35/100
40% of women = 40*65/100
total employees = 7+26 = 33 out of 100
so, Ans = 33 %
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Ques:- 3978 + 112 x 2 = ? ? 2
Recent Answer : Added by Admin On 2020-05-17 12:03:32:
( d ) 8404
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Ques:- A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. What is the speed of the train ?
Recent Answer : Added by Swaleh Mohamed On 2022-08-14 16:45:53:
Length of train = 125Mtrs
Speed of man = 5Km/Hr
=(5*1000)/(1*3600)
=1.4M/s
Time taken for train to pass = 10s
Spd = D/T
Total Distance (Man distance+ Train Length)
#Distance covered by Man in 10s
D=Spd*T
= (1.4M/s*10s)
= 14Mtrs
#Train length = 125Mtrs
Total D = 14Mtrs + 125Mtrs
= 139Mtrs
Time taken = 10s
Sp = D/t
=139M/10s
=13.9M/s
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Recent Answer : Added by Admin On 2020-05-17 11:59:57:
Ques:- There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?
Recent Answer : Added by Paul Gotti On 2022-08-14 16:28:42:
1:2
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Recent Answer : Added by DK BOSS On 2021-07-21 15:26:11:
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Ques:- A prime number N, in the range 10 to 50 remains unchanged when its digits are reversed. The square of such a number is
A. 1936
B. 1089
C. 484
D. 121
Recent Answer : Added by Killer On 2022-08-14 16:39:48:
Recent Answer : Added by NEPPALI SAI KRISHNA On 2021-11-22 18:35:05:
9
Ques:- Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group? (a) Rose (b) Lily (c) Lotus (d) Marigold (e) Apple
Recent Answer : Added by Admin On 2020-05-17 12:03:34:
( e ) Apple
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Ques:- In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily. After how many days will half of the pool be covered by the water-lily?
Recent Answer : Added by HEMANTH MOKKAPATI On 2022-03-09 16:33:21:
the pool will be half full at the 19th day .so that it doubles on the 20th day and becomes full
Ques:- Find out the wrong number in the series:
2880, 480, 92, 24, 8, 4, 4
A. 4
B. 8
C. 24
D. 92
Recent Answer : Added by Javed Walandkar On 2022-08-14 16:35:10:
Ques:- The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is
A. 50
B. 100
C. 105
D. 125
Recent Answer : Added by Pavani On 2023-05-02 06:08:20:
125
Ques:- The post office is to the east of the school while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school, in which direction is the market with respect to my school?
Recent Answer : Added by Shraddha On 2020-07-29 09:50:35:
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