Join For Education

1. Electric and magnetic forces determine the properties of atoms, molecules and bulk matter. 2. From simple experiments on frictional electricity, one can infer that there are two types of charges in nature; and that like charges repel and unlike charges attract. By convention, the charge on a glass rod rubbed with silk is positive; that on a plastic rod rubbed with fur is then negative.  3. Conductors allow movement of electric charge through them, insulators do not. In metals, the mobile charges are electrons; in electrolytes both positive and negative ions are mobile. 4. Electric charge has three basic properties: quantisation, additivity and conservation. Quantisation of electric charge means that total charge (q) of a body is always an integral multiple of a basic quantum of charge (e) i.e.,  q = n e, where n = 0, ±1, ±2, ±3, .... Proton and electron have charges +e, –e, respectively. For macroscopic charges for which n is a very large number, quantisation of charge can ...

Complex Numbers and Quadratic Equations

This chapter deals with some basic definitions and operations involving sets. These are summarised below: • A set is a well-defined collection of objects.   • A set which does not contain any element is called empty set.   • A set which consists of a definite number of elements is called finite set, otherwise, the set is called infinite set.   • Two sets A and B are said to be equal if they have exactly the same elements.   • A set A is said to be subset of a set B, if every element of A is also an element of B. Intervals are subsets of R.   • A power set of a set A is collection of all subsets of A. It is denoted by P(A).   • The union of two sets A and B is the set of all those elements which are either in A or in B.   • The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B.  • The complement of a subset A of univers...

In this chapter, we studied different types of relations and equivalence relation, composition of functions, invertible functions and binary operations. The main features of this chapter are as follows:  → Empty relation is the relation R in X given by R = φ ⊂ X × X. →  Universal relation is the relation R in X given by R = X × X. →  Reflexive relation R in X is a relation with (a, a) ∈ R  a ∈ X. → Symmetric relation R in X is a relation satisfying (a, b) ∈ R implies (b, a) ∈ R. → Transitive relation R in X is a relation satisfying (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R. →   Equivalence relation R in X is a relation which is reflexive, symmetric and transitive. →  Equivalence class [a] containing a ∈ X for an equivalence relation R in X is the subset of X containing all elements b related to a. →  A function f : X → Y is one-one (or injective) if f(x1) = f(x2) ⇒ x1 = x2  x1, x2 ∈ X. →  A function f : X → Y is onto (or sur...

Hydrocarbons are the compounds of carbon and hydrogen only. Hydrocarbons are mainly obtained from coal and petroleum, which are the major sources of energy. Petrochemicals are the prominent starting materials used for the manufacture of a large number of commercially important products. LPG (liquefied petroleum gas) and CNG (compressed natural gas), the main sources of energy for domestic fuels and the automobile industry, are obtained from petroleum. Hydrocarbons are classified as open chain saturated (alkanes) and unsaturated (alkenes and alkynes), cyclic (alicyclic) and aromatic, according to their structure. The important reactions of alkanes are free radical substitution, combustion, oxidation and aromatization. Alkenes and alkynes undergo addition reactions, which are mainly electrophilic additions. Aromatic hydrocarbons, despite having unsaturation, undergo mainly electrophilic substitution reactions. These undergo addition reactions only under special conditions. Alkanes show c...