(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) Pythagoras (569 BCE – 479 BCE) The Pythagoreans in Greece, followers of the famous mathematician and philosopher Pythagoras, were the first to discover the numbers which were not rationals, around 400 BC. These numbers are called irrational numbers (irrationals), because they cannot be written in the form of a ratio of integers. There are many myths surrounding the discovery of irrational numbers by the Pythagorean, Hippacus of Croton. In all the myths, Hippacus has an unfortunate end, either for discovering that √2 is irrational or for disclosing the secret about √2 to people outside the secret Pythagorean sect ! G. Cantor (1845-1918) & R. Dedekind (1831-1916) In the 1870s two German mathematicians, Cantor and Dedekind, showed that: Corresponding to every real number, there is a point on the real number line, and corresponding to every point on the number line, there exi
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) NCERT Class-9 Maths Chapter-15:Probability Questions with step-by-step answers Exercise-15.1 1. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. 2. 1500 families with 2 children were selected randomly, and the following data were recorded: Compute the probability of a family, chosen at random, having (i) 2 girls (ii) 1 girl (iii) No girl Also check whether the sum of these probabilities is 1. 3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August. 4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: If the three coins are simultane
Click on the link to reach the MCQ's and solutions (consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) MCQ's (100 each) :- Digital Documentation class 10 MCQ Questions Electronic Spreadsheet Advanced Class 10 MCQ RDBMS Class 10 MCQ Questions ICT Skills (part-A) MCQ's Self Management Skills (part-A) MCQ's Book Solutions :- Digital Documentation Book Solutions Electronic Spreadsheet (Advanced) Book Solutions RDBMS(Basic) Book Solutions click on the follow button to get instant notification on upload of new mcq's
IT TERM-2 STUDY MATERIAL (consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) BOOK SOLUTIONS:- RDBMS WEB APPLICATION AND SECURITY NOTES:- RDBMS WEB APPLICATION AND SECURITY ENTREPRENEURIAL SKILLS GREEN SKILLS IMPORTANT QUESTIONS:- RDBMS SESSION-1 SESSION-2 SESSION-3 SESSION-4 SESSION-5 WEB APPLICATION AND SECURITY SESSION-1 SESSION-2 SESSION-3&4 SESSION-5&6 SESSION-7 SESSION-8 SESSION-9 SESSION-10 SESSION-11 ENTREPRENEURIAL SKILLS GREEN SKILLS SAMPLE QUESTION PAPER:- SQP Marking scheme
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) Exercise-1.1 1. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. 3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? 4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.] 5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8. Answers:-
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) NCERT Class-10 Maths Chapter-2:Polynomials Questions with step-by-step answers Exercise-2.2 Answers:- Exercise-2.3 Answers:- Exercise-2.4 (optional) Answers:- Extra Sums Worksheet - 1 Answers:- Worksheet - 2 Answers:-
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) NCERT Class-9 Maths Chapter-13:Surface Area and Volume Questions with step-by-step answers Exercise-13.1 Answers:- Exercise-13.2 Answers:- Exercise-13.3 Answers:- Exercise-13.4 Answers:- Exercise-13.5 Answers:- Exercise-13.6 Answers:- Exercise-13.7 Answers:- Exercise-13.8 Answers:- Exercise-13.9 (Optional) Answers:-
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) NCERT Class-9 Maths Chapter-12:Heron's Formula Questions with step-by-step answers Exercise-12.1 Answers:- Exercise-12.2 Answers:-
(consider clicking the follow button for our efforts. It is similar to subscribe in YouTube) 1. Mu hammad ibn Musa al-Khwarizmi (C.E. 780 – 850) An algorithm is a series of well defined steps which gives a procedure for solving a type of problem. The word algorithm comes from the name of the 9th century Persian mathematician al-Khwarizmi. In fact, even the word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabr w’al-muqabala. A lemma is a proven statement used for proving another statement. 2. Carl Friedrich Gauss (1777 – 1855) An equivalent version of Theorem 1.2 (refer book) was probably first recorded as Proposition 14 of Book IX in Euclid’s Elements, before it came to be known as the Fundamental Theorem of Arithmetic. However, the first correct proof was given by Carl Friedrich Gauss in his Disquisitiones Arithmeticae. Carl Friedrich Gauss is often referred to as the ‘Prince of Mathematicians’ and is considered one of the three greatest mathematician
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