An Useful Article on Number system i found on Bulls Eye Website.
Unit Digit of A Number
The concept that revolves around finding the unit digit of a number uses the basics of number system. Learning this concept means you have strengthened your basic concepts.
The concept of unit digit can be learned by figuring out the unit digits of all the single digit numbers from 0 - 9 when raised to certain powers. The first learning in that for you will be that these numbers can be broadly classified into three categories for this purpose:
Digits 0, 1, 5 & 6: When we observe the behavior of these digits, they all have the same unit's digit as the number itself when raised to any power, i.e. 0n = 0, 1n =1, 5n = 5, 6n = 6. So, it becomes simple to understand this logic.
Examples: Finding the Unit digit of following numbers:
185563 = 5; 2716987 = 1; 15625369 = 6; 190654789321 = 0.
Digits 4 & 9: Both these numbers are perfect squares and also have the same behavior with respect to their unit digits i.e. they have a cyclicity of only two different digits as their unit's digit.
Have a look at how the powers of 4 operate:
41 = 4, 42 = 16, 43 = 64 and so on.
Hence, the power cycle of 4 contains only 2 numbers 4 & 6, which appear in case of odd and even powers respectively.
Likewise 91 = 9, 92 = 81, 93 = 729 and so on.
Hence, the power cycle of 9 also contains only 2 numbers 9 & 1, which appear in case of odd and even powers respectively.
So broadly these can be remembered in even and odd only, i.e. 4odd = 4 and 4even = 6 and likewise 9odd = 9 and 9even = 1.
Examples: Finding the Unit digit of following numbers:
189562589743 = 9 (since power is odd); 279698745832 = 1(since power is even);
154258741369 = 4 (since power is odd); 19465478932 = 6 (since power is even).
Digits 2, 3, 7 & 8: These numbers have a power cycle of 4 different numbers
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A. While caste discrimination is banned, caste associations may be difficult to proscribe.
B. In these circumstances, caste rallies cannot be proscribed by judicial fiats, not because they are prone to misapplication but because the Constitution guarantees all forms of social association.
C. However, it also protects against discrimination on the grounds of religion, creed, caste and gender.
D. This is a subtle distinction that needs to be kept in mind.
E. And in certain circumstances, positive caste discrimination in favour of historically disadvantaged groups is permitted too.
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1. India, which has two out of every five TB patients in the world, is on the brink of a major public health disaster.
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@angadsharma said:Set-1A. After doing so, the heart of your cash flow will be strong and healthy.B. Cash is your businesss lifeblood.C. If managed poorly, then your company could go into cardiac arrest.D. To prevent your business from suffering heart attacks, you should learn to manage cash flow in a well thought-out manner.E. Several ways to do this is by generating a project rate of returns as well as determining possible problems with liquidity.a) ABECD b) CBADE c) BCDEA d) ABDECSet-2A. This factor is exclusion access to these technologies remains excluded by class, race and gender.B. In comparing these two things, we must realize that there is one important factor for the limitation the former.C. The rise of digital technologies has the potential to open new directions in ethnography.D. Despite the ubiquity of these technologies, their infiltration into popular research methods is still limited compared to the number of online scholarly research portals.a) CDBA b) BACD c) CDAB d) BCDASet-3A. Adam Smith is often described as the founding father of economics.B. One prominent book he wrote was Theory of Moral Sentiments.C. A great deal of what is now considered standard theory about markets was developed by Adam Smith.D. It is a very important text in the history of moral and political thought because he talks about individual freedom.E. According to Smith, this freedom is rooted in self-reliance and the ability of an individual to pursue his self-interest.a) EDACB b) ACBED c) ACBDE d) EBADESet-4A. Today, the study of the fruit fly has expanded to research for human diseases.B. This is because the fruit flys robust genetic system makes it an invaluable tool for scientists studying current inheritance diseases.C. These diseases include Alzheimers, Parkinsons and Huntingtons disease.D. In past decades, scientists have used the fruit fly as a model organism for examining biological systems.a) DACB b) DABC c) BACD d) CBADSet-5A. It is one of a group of disorders known as parasomnias: unusual activities that occur during sleep.B. Sleepwalking occurs in the deep stage of sleep when slow brain waves begin to appear.C. These range from teeth grinding and restless leg syndrome to eating while asleep.D. Our bodies function according to a 24 hour cycle called a circadian rhythm.E. Some researchers believe that slight differences in this cycle could be linked to sleepwalking.a) BACED b) CDBAE c) EBACD d) BACDE
A. French conceptual artist Sophie Calle photographed the sites of vanished communist monuments in East Berlin and then asked locals to describe what had been there.
B. The German superstar Thomas Demand modelled, then photographed, a miniature Stasi office with its drawers frantically rifled.
C. There are exceptions, mostly concerning only one side of the Wall.
D. Jane and Louise Wilson simply videoed the real building, showing its cruddy furniture and primitive spying equipment, including a false tree trunk with eyeholes, offering no political insights
6. Collective memory divided by tyranny!