A list consists of the following pairs of numbers: `51, 53;` `55,57;` `59,61;` `63,65;` `67,69;` `71,73`
Categorize them as pairs of:
(i) co-primes          
(ii) primes        
(iii)  composites

From the list below, form 17 pairs of co-prime numbers: 3,5, 6,7, 12, 18, 24, 25

Show that the following pairs are co-prime: (i) 59, 97 (ii) 875, 1859 (iii) 288, 1375

Which of the following pairs are always co-primes? (i) two prime numbers (ii) one prime and one composite number (iii) two composite numbers

Column I ; Column II {2,3} ; p. is a pair of primes {11 ,13} ; q. is a pair of twin primes {5,11} ; r. is a pair of co-primes {2,6} ; s. is a pair of even number

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly two divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number having more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Number of composite numbers less than 15 is "(a) 10 (b) 9 (c) 8 (d) 7"

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly tow divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number habing more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Let p & q be the number of natural numbers which are less than or equal 20 and are prime & composite respectively, then 20-p-q is equal to "(a) 1 (b) 0 (c) 2 (d) 3"

Express each of the following in terms of angles between 0^(@) and 45^(@) (i) sin 59^(@) + tan 63^(@) (ii) "cosec 68"^(@) + cot 72^(@) (iii) cos 74^(@) + sec 67^(@)

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly two divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number having more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Number of prime numbers less than 10 is "(a) 2 (b) 3 (c) 4 (d) 5 "