Tips Tricks Knowledge

 About 13.7 billion years ago the universe was formed in a massive explosion called The Big Bang . The Universe consists of everything that exists:  Matter Space Time Energy All of the above are part of the universe . Energy is of various types: light, sound, motion and even heat. Matter, on the other hand, can be easily seen with the naked eye . All the objects around us are made up of matter.  Even today, the universe continues to expand , cool and change. This phenomenon was discovered by the American astronomer, Vesto Slipher in the 1910. Big Bang➡️ 200 million years after Big Bang➡️ Formation of stars➡️ 500 million years after the Big Bang➡️ Formation of galaxies➡️ 1 billion years after Big Bang➡️ Galaxies with different shapes exist in the universe➡️ 9 billion years after Big Bang➡️ Formation of our solar system

      Good English is an essential part of your essays. Good English is an asset if you are to make anything clear. If you cannot write good English you are always at a disadvantage.       Language is the vehicle of thoughts. Without the power of ready expression you cannot make real progress, since a poor vocabulary prevents you from giving a true impression of your personality to people whose opinion is of great importance to you.       The secret of writing good English does not lie in memorizing the rules of grammar, but in developing the habit of clear thinking. " Probably the greatest social value of good English training is the feeling of self confidence which follows it ".        Good English enables you to make the most of your abilities. The man who can speak and write fluently and expressively, who can give a proper impression of his personality and is not held back by the fear that his good Englis...

Sum of first 'n' number of natural numbers Choose any set of natural numbers starting with '1'. Multiply the last number to the next number. Then divide the product by two. Example: Sum of first 10 natural numbers = [10(10+1)]/2 = (10*11)/2      = 110/2            = 55                Sum of first 100 natural numbers = [100(100+1)]/2 = (100*101)/2      = 10100/2            = 5050                 Proof Sn = n/2(a+l) => Sn = n/2(1+n)     => Sn = n(n+1)/2     where, Sn = Sum                                        n = number of terms              l = last term = n Average of first 'n' number of natural...

Numbers that end in '5' Choose any number that ends in 5. Remove '5' from the number. Multiply the left number to its predecessor (next number). Then write '25'. Example: (45)^2 = Remove 5 from the number. The number left is '4'. Multiply 4 with its next number i.e. 5. and write 25 1. (45)^2       = 4(4+1)|25   = 4(5)|25  = 20|25  = 2025   2. (65)^2        = 6(6+1)|25    = 6(7)|25 = 42|25  = 4225   Proof (10n+5)^2                      = (10n)^2+2*10n*5+(5)^2           = 100n^2+100n+25       = (n^2+n)100+25        = [n(n+1)]100+25  = n(n+1)|25      Numbers near to '50' (25-75) To help you I recommend you to memorize some squares :- 1,2,3,4,5,............,23,24,25,50,100 Choose any number between ...