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Q.No. 1 & 2 Paper 2 2026

To locate the position of an object or a point in a plane, we require  two perpendicular lines — One of them is horizontal, and the  other is vertical. z The plane is called the cartesian plane, the coordinate plane or  the xy-plane and the lines are called the coordinate axes. z The horizontal line is called the x-axis and the vertical line is  called the y-axis. z The coordinate axes divide the plane into four parts called  quadrants. z The point of intersection of the axes is called the origin. z The distance of a point from the y-axis is its x-coordinate and  the distance of the point from the x-axis is its y-coordinate. If the  x-coordinate of a point is x, and the y-coordinate is y, then (x, y)  are called the coordinates of the point. The coordinates of a point on the x-axis are of the form (x, 0), and  those of the points on the y-axis are of the form (0, y). z The coordinates of the origin are (0, 0). z The coordinates of a point are...

Inverse Trigonometric Functions Exemplar XII 30 to 37

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...