Competitive Friend

 Shakespeare termed India  the Land of Opportunities. Hagel called India as Land of Desire. There were three trade routes to India through Caspian and Black sea, another from the Mediterranean sea, and another from Egypt via the Red Sea. All the route was closed due to the defeat of Constantinople by Turkey. The Portuguese: In 1498 Vasco Da Gama reach Calicut during the reign of King Zamorin. They Established Taxde centers in Calicut, Cochin, and cannivore. Cochin was the Initial capital of the Portuguese but later it was replaced by Goa. The First Portuguese Governor was Fransisco de Almedia and he introduced the Policy of Bluewater (as  opposed to establishing a territorial empire in India and wanted the Portuguese should maintain supremacy on the sea and confine their activities to purely commercial transactions. This policy is known as the Bluewater policy.)  In 1509 The Portuguese Governor Alfanso de Albuquerque   The policy of Imperialism. ( Portuguese Go...

Rules of counting numbers: 1. Sum of all first natural numbers: = {n(n+1)}/2 Ex 1 Sum od 1+2+3+....100= {100(100+1)}/2=50*101 =5050 2. Sum of first n  odd Numbers= n^2 (where "n" is numbers) Ex. 1+3+5+...20th odd numbers= 20^2= 400 3. Sum of first n even numbers= n(n+1) Ex. Sum of 2+4+6... 100= 50 th even numbers then =50(50+1)= 2550 4. Sum of square of first n numbers ={n(n+1)(2n+1)}/6 Ex. 1 to 10th sqare sum is {10(10+1)(2*10+1)}/6 5. Sum of Cube of first numbers= [{n(n+1)}/2]^2 Ex. 1 to 6 cube sum = [{6(6+1)}/2]^2 = 21^2= 441 In the first n counting number if n is even the number of odd numbers is n/2 and the even number is also n/2.\ If the first n counting number is odd the number of odd numbers is (n+1)/2 and the even number is (n-1)/2. Ex.  Rule-2 Difference between squares of all consecutive numbers is always an odd number. Ex: 4^2 and 5^2. difference is 25-16=9 = odd number Rule-3 Difference between squares of consecutive numbers is the sum of these numbers. Ex. 5^2-...