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Base System: Problem part - 5
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Base System problem part - 5

## Bharat Gupta is teaching live on Unacademy Plus

Bharat Gupta
Engineer by degree Mathematician by Heart. Having 22 years of teaching experience. Search me on Youtube for more videos.

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Great work Shoaib. I detest reading the Yojana, however, these videos make it considerably easier and interesting. For all those people who are in the same boat: see the video, jot down the points and then read the corresponding articles. Works wonders!
there is a mistake in first question. it should be 19257 because 110100 in base 7 is equal to 19257
Sir, in the first question, using your previous concept explanation, the much faster approach will be - - -> Given binary number has 2 trailing zeros, therefore, the factor which is repeated twice (here 7 in the number 19527) will be base for 110100. Is this approach correct?
1. Base System Problems part 5

2. Normally, numbers are written with base 10. Binary numbers have a base of 2. If 19527 = 3 * 7 * 7 * 131, in what base can be written as 110100? a. 3 b.5 C7 How many numbers (in base 10) are there such that base 8 representation and base- 12 representation of the numbers are both three-digit numbers? a. 367 b. 368 c. 461 d. 462 d. 8 How many numbers have exactly 3 digits when expressed in either base 5 or base 11? A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true? a. a must be 2 b. c must be 2 c. b must be 0 d. None On planet Jupiter the people use a certain number system to the base 'n' (n > 2), Mark, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of 'n' is the least possible value. Then the decimal representation of the difference between Mark's correct and wrong wage for the day is a. 18 b. 8 c. 27 d. 9

3. Normally, numbers are written with base 10. Binary numbers have a base of 2. If 19527 = 3 * 7 * 7 * 131, in what base can be written as 110100? c. 7 d. 8

4. Normally, numbers are written with base 10. Binary numbers have a base of 2. If 19527 = 3 * 7 * 7 * 131, in what base can be written as 110100? c. 7 d. 8 o loo = 49 (393)

5. How many numbers have exactly 3 digits when expressed in either base 5 or base 11? a. b. 2 C. 5 d. 7

6. How many numbers have exactly 3 digits when expressed in either base 5 or base 11? a. b. 2 C. 5 d. 7 No.ur lolaere wlumao, nvuti. Alo S-baal 10tove thre

7. How many numbers have exactly 3 digits when expressed in either base 5 or base 11? a. 4 b. 5 C. 6 d. 7 oi0 hove tue Lon O l ll bese 121 133D

8. How many numbers have exactly 3 digits when expressed in either base 5 or base 11? a. 4 b. 5 C. 6 d. 7 23 tt bese 1330 121 Cowwon ko. 121,122, 123, l29

9. How many numbers (in base 10) are there such that base - 8 representation and base 12 representation of the numbers are both three-digit numbers? a. 367 b. 368 c. 461 d. 462

10. How many numbers (in base 10) are there such that base - 8 representation and base 12 representation of the numbers are both three-digit numbers? a. 367 b. 368 c. 461 d. 462 2 han -9 9 172 baan _ 12 12 123-1 144 sll bn -12 1vy = 511-143 = 36 b