Class 11 Cheatsheet (Science)

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Mathematics: Limit and Continuity

Limits A function f(x) is said to have a limit at l at point a when f(x) approaches to l whenever x approaches to a. (lim)┬(x→a) ⁡ f(x)=l Important Theorem on Limit For all rational values of n, (lim)┬(x→a) ⁡ 〖 (x^n-a^n)/(x-a) 〗 =na^(n-1) Case 1: When n is a positive integer: By actual division, (x^n-a^n)/(x-a)= x^(n-1)+x^(n-2).a+x^(n-3).a^2+…+a^(n-1) Now, (lim)┬(x→a) ⁡ 〖 (x^n-a^n)/(x-1) 〗 = (lim)┬(x→a) ⁡ [x^(n-1)+x^(n-2).a+x^(n-3).a^2+…+a^(n-1) ] = a^(n-1)+a^(n-1)+a^(n-1)+…+a^(n-1) = na^(n-1)

English (Magic of Words) : The Loving Mother

Summary "The Loving Mother" is a supernatural story that is brought from Island of Hokkaido, Japan. The main character of this story is a pharmacist who found a mysterious woman coming to his drugstore every night asking the same thing. Finally, this woman appears to be the spirit of a mother who is dead and her child is alive alone. Shoji Sakota, the pharmacist was working on his annual business report on a stormy winter night. Then finally, a woman came in a mysterious way. She was like she came from another world. She came in the second night and the third night too on the same hair, same dress, same time and asking the same thing for her baby i.e. ame on a stick. On the fourth night, Shoji Sakota kept a photographer friend in the drugstore. After the photos were developed, the woman was not seen. So, they decided to follow the mysterious woman the next night. So, they followed her. The woman knew that they were following her. So, she let them follow. Then she wen...

Physics: Electric Charge

This lesson teaches you about various aspects of electric charge, their attraction and some laws related to it. Electric Charge The electric charge is the intrinsic property of fundamental particle which is responsible for electric force due to which two bodies to attract or repel with each other. Electric charge is of two types: Positive Charge and Negative Charge. A body becomes positively charged when it loses electrons and becomes negatively charged when it gains electrons. Two bodies having similar charge repel with each other and opposite charge attract each other. Pair of Objects Charge Developed Positive Negative 1. Glass rod and silk Glass Rod Silk 2. Ebonite Rod and Fur Fur Ebonite Unit of Electric Charge Electric Charge (q) = It So, unit charge is (A-s) also called coulomb (c) and in CGS system is stat coulomb. Dimensional Formula = [AT] 1c =...

Chemistry: Atomic Structure

This chapter teaches about how various components make an atom and how they behave and what is the secret behind such structure of atoms. In 1804, John Dalton provided Atom's Postulations and it is called Dalton's Atomic Theory The word 'Atom is derived from the Greek word which means 'indivisible'. That means it cannot be further broken down into ["atomos"] Postulates of Dalton's Atomic Theory All matters are composed of very minute particles which are called atoms. Atom can neither be created nor be destroyed by any physical and chemical method. The atom of the same elements is identical in all respect. That means their shape, size,... are same. Atoms of different elements are different in all respect. Atoms of same or different elements combines in a fixed ration or simple whole number to give compound atom. Discovery of Electron Cathode Ray Experiment Towards the end of the 18th century, JJ Thompson performed cathode rays...