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Consider the mathematical statements: 2. $n(n+1)$ is divisible by 2. 2. $3^{2n}-1$ is divisible by 8. 3. $n^2-n+41$ is a prime integer. 4. If a set S contains n distinct objects, then the number of subsets of S is $2^n$. All these statements are concerned with natura..

% 0% transparent;"> we -1 3 o __ A 3 cos = 0 => cos8= - / -1 3-\ / - -1.4 V 4 sin I cos -j = sin I sin I = K '..

In day to day life we use words like a pack of cards, a foot ball team, and herd of sheep to denote collection of objects of a particular kind. In mathematics, we come across words like natural numbers, lines, composite numbers Let us examine some collections: Vowels in Engli..

Solution: Let n(M) = number of students who secured first class marks in Mathematics n(E) = number of students who secured first class marks in English n(M) = 70 n(M $\cup$ E) = 120 n(M $\cap$ E) = 31 Using n(M $\cup$ E) = n(M) + n(E) - n(M $\cap$ E) ..

">In a solution containing n A moles of solute and n B moles of solvent, the mole fraction of solute, X A , and the moie fraction of the solvent, X . can be expressed as follows: x=n/a/n/a/n/a mass percent = the percent of a solution's total mass that is ..

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Age Word Problems 4:A father and his son are 36 years and 6 years old respectively. In how many years will the father be thrice as old as his son? Solution: We have to find the number of years in which, father will be thrice as old as his son. Let us set up an equation. Let x b..

guiding Questions What is science? How is science different from non-science disciplines? What is ^ chemistry? What does it do? What are laws of nature? What is an experiment? Why r is it important to conduct experiments in science? What is a hypothesis? How is it Qiffererit from spec..