1 . Make clear any encryption- decryption approach. Use it to encrypt and decrypt ‘INDIA IS MY OWN COUNTRY'. Ans:

2 . Make a grid of natural numbers via 400-500. Find all the excellent numbers inside the grid. Determine all pairs of cal king primes in the grid you have made. Can easily all the excellent numbers determined by you in the grid be symbolized as 6n-1 or 6n+1, where and is a all-natural number? Warrant your solution. Ans:

Here is how to prove the observation: have any integer n greater than three or more, and divide it by simply 6. � That is, create n = 6q + r

Where q is a nonnegative integer plus the remainder r is among 0, you, 2, a few, 4, or perhaps 5. In case the remainder can be 0, 2 or four, then the number n is divisible by simply 2, and cannot be perfect. If the rest is a few, then the number n is divisible by 3, and cannot be primary. So if n is prime, then your remainder r is possibly

1 � (and n = 6q + 1 � is an additional than a multiple of six), or 5 � (and n = 6q + 5 = 6(q+1) - 1 � is definitely one just one multiple of six). Do not forget that being yet another or much less, than a multiple of 6 does not produce a number perfect. � We certainly have only proven that all prime other than 2 and several (which split 6) have this form. four hundred

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3. Permit p be any perfect number and a& w be virtually any two organic numbers. Warrant what all possible values a and b decide on satisfy a)

b)

c)

d)

4. Categorize subsequent into Principal and Supplementary data resources:

Magazines----- Secondary

Newspaper----- Secondary

Journals--------- Secondary

Telephone------ Primary

Interview------ Primary

Questionnaire-- Primary

Survey----------- Primary

Standard Reports--- Secondary

Internet------------ Secondary

Official Websites--- Secondary

5. Justify selecting a mean, mode or median in the next cases:

A shopkeeper needs to inventory his store with different designs of chocolates. This individual does a survey in his area about the preferences of people and needs to determine the brand that he should place maximum order.

ANS: He should work with mode since it would give the rand name the maximum number are using and his sale would be the maximum thus the profit.

Assume an And. G. Um. wants visitors light to become put up for a bridging. They accumulate data of number of autos passing the crossing on each of your day and desires to convince the appropriate power.

ANS: This individual should make use of mean, mainly because it would give the regular value with the number of cars passing throughout the day. Mode is usually not convenient as it gives the day together with the largest range of cars and median the afternoon with the when the number of cars is in the midsection of any kind of series.

6. Discuss a few situations where Gambler's argument is experienced. ANS:

The gambler's argument, also known as the Monte Carlo fallacy or perhaps the fallacy from the maturity of chances, may be the mistaken idea that in the event that something happens more frequently than normal during some period, then it will happen less frequently in the future. Likewise, if some thing happens much less frequently than normal during some period, then it may happen more frequently down the road (presumably as a way of controlling nature). In case of where precisely what is being discovered is truly random (i. e. independent trials of a unique process), this belief, though appealing to the human mind, is usually false. This fallacy can arise in several practical conditions although it is most strongly connected with gambling where such blunders are common among players.

CASES

1 . Childbirth

Instances of the...