HISTORY PDF DIGEST

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Easy way to understand Direct and Indirect speech rules

Introduction. There two ways to convey a message of a person, or the words spoken by a person to other person. 1. Direct speech 2. Indirect speech Suppose your friend whose name is Vipul tells you in College , “I will give you a pen”. You come to home and you want to tell your brother what your friend told you. There are two ways to tell him. Direct speech: Vipul said, “I will give you a pen”. Indirect Speech: Vipul said that he would give me a pen. In direct speech the original words of person are narrated (no change is made) and are enclosed in quotation mark. While in indirect speech some changes are made in original words of the person because these words have been spoken in past so the tense will change accordingly and pronoun may also be changed accordingly. In indirect speech the statement of the person is not enclosed in quotation marks, the word “ t...

English Error Spotting - Previous Year Questions of SSC CGL

Competition Zenith brings you a post on Error Spotting to boost your English for competitive exams. We are providing you the specifically chosen questions from previous year papers of SSC CGL with the best possible explanation in simplest of the language. Below are some questions with explanation: Questions 1. Have trust on(a)/God and everything(b) /will be right.(c) /(d) No error 2. The cattles (a) /are grazing (b) /in the fields.(c) /(d) No error 3. He is one of (a)/ the best novelists (b) /that has ever lived. Do you agree? (c)/no error (d) 4. On a rainy day (a) /I enjoy to watch TV (b) / with a hot cup of tea.(c ) /no error(d) 5. No sooner did (a)/I reach (b)/ Patna railway station than the train departed(c)/no error (d) 6. There is no agreement (a) / between you and I (b) /so we are free to go our way(c) /no error (d) 7. A variety of books (a) / is available in the market (b) / to help the students qualify the competitive examinations.(c) /no error 8....

Trigonometry And Its Short Tricks

Trigonometric Function Trigonometric Functions (Right Triangle) Special Angles Trigonometric Function Values in Quadrants II, III, and IV Examples: Example2: Example: 3: Unit Circle Addition Formulas: cos(X+Y) = cosXcoxY – sinXsinY cos(X-Y) = cosXcoxY + sinXsinY sin(X+Y) = sinXcoxY + cosXsin sin(X-Y) = sinXcoxY – cosXsinY tan(X+Y) = [tanX+tanY]/ [1– tanXtanY] tan(X-Y) = [tanX-tanY]/ [1+ tanXtanY] cot(X+Y) = [cotX+cotY-1]/ [cotX+cotY] cot(X-Y) = [cotX+cotY+1]/ [cotX-cotY] Sum to Product Formulas: cosX + cosY = 2cos [(X+Y) / 2] cos[(X-Y)/2] sinX + sinY = 2sin [(X+Y) / 2] cos[(X-Y)/2] Difference to Product Formulas cosX - cosY = - 2sin [(X+Y) / 2] sin[(X-Y)/2] sinX + sinY = 2cos [(X+Y) / 2] sin[(X-Y)/2] Product to Sum/Difference Formulas cosXcosY = (1/2) [cos (x-Y) + cos (X+Y)] sinXcoxY = (1/2) [sin (x+Y) + sin (X-Y)] cosXsinY...

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