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Definition of set: A set is a collection of well-defined objects. Explanation of the term “Well-defined”: Well-defined means, it must be absolutely clear that which object belongs to the set and which does not. Now, to get basic concepts of sets about the meaning of well-defined the following examples are given below. 1.  The collection of vowels in English alphabets. This set contains five elements, namely, a, e, i, o, u. 2.  A group of “Singers with ages between 18 years and 25 years” is a set, because the range of ages of the singer is given and so it can easily be decided that which singer is to be included and which is to be excluded. Hence, the objects are well-defined. 3.  A collection of “Red flowers” is a set, because every red flowers will be included in this set i.e., the objects of the set are well-defined. .  The collection of past presidents of the United States union is a set. 5.  A group of “Young dancers” is not a set, as the range of the ages of young dancers is not g

                     Trigonometry                   To find the distances and heights we can use the mathematical techniques, which come under the  Trigonometry . It shows the relationship between the sides and the angles of the triangle. Generally, it is used in the case of a right angle triangle. Trigonometric Ratios In a right angle triangle, the ratio of its side and the acute angles is the trigonometric ratios of the angles. In this right angle triangle ∠B = 90°. If we take ∠A as acute angle then - AB is the base , as the side adjacent to the acute angle. BC is the perpendicular , as the side opposite to the acute angle. Ac is the hypotenuse , as the side opposite to the right angle. Trigonometric ratios with respect to  ∠A                        sin (90° – A) = cos A, cos (90° – A) = sin A, tan (90° – A) = cot A, cot (90° – A) = tan A, sec (90° – A) = cosec A, cosec (90° – A) = sec A     All formula of Trigonometry:

                                        Integers                                                 A whole number, from zero to positive or negative infinity is called  Integers . I.e. it is a set of numbers which include zero, positive natural numbers and negative natural numbers. It is denoted by letter Z. Z = {…,-2,-1, 0, 1, 2…}  Integers on Number Line On the number line, for positive integers we move to the right from zero and for negative integers move to the left of zero                                             Facts about how to Add and Subtract Integers on the Number Line: 1. If we add a positive integer, we go to the right. 2. If we add a negative integer, we go to the left. 3. If we subtract a positive integer, we go to the left. The Additive Inverse of an Integer The negative of any number is the additive inverse of that number. The additive inverse of 5 is (- 5) and additive inverse of (- 5) is 5. This shows that the number which we add to a number to get zero is the add

  Chemical reactions -   The transformation of chemical substance into a new chemical substance by making and breaking of bonds between different atoms is known as Chemical Reaction.  Signs of a chemical reaction These factors denote that a chemical reaction has taken place- change of state of substance, change of color of substance,evolution of heat, absorption of heat, evolution of gas and evolution of light. Chemical Equation:   The representation of chemical reaction by means of symbols of substances in the form of formulae is called chemical equation.  E.g. - H 2  + O 2  ⇒ H 2 O                        Balanced Chemical Equation:   A balanced chemical equation has number atoms of each element equal on both left and right sides of the reaction.                                    *Note- According to Law of Conservation of Mass, mass can neither be created nor destroyed in a chemical reaction. To obey this law, the total mass of elements present in reactants must be equal to the total