GRAPH OF FUNCTIONS


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To draw the graph for any function, we need to take some positive and negative values of then find the corresponding values of And make the line or curve by joining the points obtained. (1) Straight Line . (2) Circle   where are co-ordinates of centre and is the radius of the circle. (3) Parabola Read More

PROPERTIES OF LOGARITHM


Properties of log

Logarithms are very useful for lengthy calculation. There are two types of logs: (1)  log   (2)  ln (Natural log) (1) The base is 10 in log (2) The base is e in natural log Here, we will discuss the properties of log. Some important properties with example are given below: If then NOTE: Example 1: Read More

WHY sin x AND cosec x ARE POSITIVE IN SECOND QUADRANT?


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जब भी मै बच्चो से पूछता हूँ कि sin x and cosec x, IInd quadrant में positive क्यों होता है? cos x and sec x, IVth में और tan x and cot x IIIrd में? हमेशा answer आता हैं, Sir, ALL SCHOOL TO COLLEGE OR ADD SUGAR TO COFFEE, etc. कुछ ही बच्चों को इसका Read More

TRIGONOMETRY FORMULAE


Trigonometry Formulae: Don’t try to remember just know the concept of derivation With the help of sin (A + B), we can derive all the remaining trigonometric formulae. Let’s see, how ….. Compound Angle (1) (2) (3) (4) (5) Dividing Numerator and Denominator by (6) Similarly, (7) (8) Transformation Formulae: By adding (1) and (2), Read More

MULTIPLICATION TECHNIQUES


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Let us consider two digit numbers ab and cd. For example: 23 × 45 Now, Now, we can try in one step.

OPERATIONS ON SETS


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(1) Union of Sets: The union of two sets A and B is the set of all the elements which are either in A or in B or in both A and B. It is denoted by . Let (2) Intersection of Sets: The intersection of two sets A and B is the set of Read More

LAWS OF SET OPERATIONS


(1) Idempotent laws : (2) Identity laws: (3) Commutative laws: (4) Associative laws: (5) Distributive Laws: (6) De-Morgan’s Laws:

CARDINAL NUMBER OF SETS


Some important results derived from Venn diagrams are as follows: A, B and C are three sets. A and B are disjoint sets.

VENN DIAGRAM


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The pictorial representation of sets is called Venn diagram. The universal set is represented by a rectangular region and its subsets by circles inside the rectangle. In the above given Venn diagram, and and .   Here,and . If, there is no common elements in A and B and both are subsets of universal set, Read More