MATHS FYUP QUESTION BANK

1. Explain any encryption- decryption technique. Use it to encrypt and decrypt ‘INDIA IS MY COUNTRY’.
Ans:

2. Make a grid of natural numbers from 400-500. Find all the prime numbers in the grid. Identify all pairs of twin primes in the grid that you have made. Can all the prime numbers identified by you in the grid be represented as 6n-1 or 6n+1, where n is a natural number? Justify your answer.
Ans:
Here is how to prove your observation: take any integer n greater than 3, and divide it by 6. That is, write n = 6q + r
Where q is a non-negative integer and the remainder r is one of 0, 1, 2, 3, 4, or 5.
If the remainder is 0, 2 or 4, then the number n is divisible by 2, and cannot be prime.
If the remainder is 3, then the number n is divisible by 3, and cannot be prime.
So if n is prime, then the remainder r is either
1 (and n = 6q + 1 is one more than a multiple of six), or
5 (and n = 6q + 5 = 6(q+1) - 1 is one less than a multiple of six).
Remember that being one more or less, than a multiple of six does not make a number prime. We have only shown that all primes other than 2 and 3 (which divide 6) have this form.
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3. Let p be any prime number and a&b be any two natural numbers. Justify what all possible values a and b take to satisfy
a)
b)
c)
d)

4. Categorize following into Primary and Secondary data sources:

Magazines----- Secondary Newspaper-----