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### How to manage the revision for Board and JEE Main Examinations

Since last two years, JEE Main (Engineering Entrance) exam conducted twice in a year. Now students are very confused about the preparation of pre-boards, boards and JEE Main. CBSE board and JEE Main dates are announced and there is approximately 15 days gap in board and JEE Main April exam. According to our opinion, we […]

### GRAPH OF FUNCTIONS

To draw the graph for any function, we need to take some positive and negative values of $$\displaystyle x,$$ then find the corresponding values of $$\displaystyle y.$$ And make the line or curve by joining the points obtained. (1) Straight Line $$\displaystyle \left( Ax+By+C \right)=0$$. (2) Circle $$\displaystyle \left[ {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \right]$$ […]

### LAWS OF SET OPERATIONS

(1) Idempotent laws : $$\text{A}\cap \text{A}=\text{A}$$ $$\text{A}\cup \text{A}=\text{A}$$       (2) Identity laws: $$\displaystyle \text{A}\cap U\text{=A}$$ $$\text{A}\cup \phi =\text{A}$$       (3) Commutative laws: $$\text{A}\cup \text{B}\,\text{=}\,\text{B}\cup \text{A}$$ $$\text{A}\cap \text{B}\,\text{=}\,\text{B}\cap \text{A}$$     (4) Associative laws: $$\left( \text{A}\cup \text{B} \right)\cup \text{C}\,=\text{A}\cup \left( \text{B}\cup \text{C} \right)$$ $$\text{A}\cap \left( \text{B}\cap \text{C} \right)=\left( \text{A}\cap \text{B} \right)\cap \text{C}$$ […]

### CARDINAL NUMBER OF SETS

Some important results derived from Venn diagrams are as follows: A, B and C are three sets. $$\displaystyle n\left( \text{A}\cup \text{B} \right)=n\left( \text{A} \right)+n\left( \text{B} \right)-n\left( \text{A}\cap \text{B} \right)$$ $$\displaystyle n\left( \text{A}\cup \text{B} \right)=n\left( \text{A} \right)+n\left( \text{B} \right)\Leftrightarrow \,$$ A and B are disjoint sets. $$n\left( \text{A}-\text{B} \right)=n\left( \text{A} \right)-n\left( \text{A}\cap \text{B} \right)$$ \(\displaystyle n\left( […]

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