Set theory Assignment – 2 Set theory Assignment is the method to make the set theory perfect. The best way to develop the required skills is that practice sufficient assignment on the topic Set theory. Question 1. 1. If A and B be two sets such that n(A)=3 and n(B)=6. Find (i) Minimum number of […]
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Equation of pair of straight line. What does concept of pair of straight line represent. Let $L_1\,:\,a_1x+b_1y+c_1=0$ and $L_2\,:\,a_2x+b_2y+c_2=0$ be two lines, then pair of straight line (also called as combined equation of given lines) […]
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Area of a parallelogram. The area of a parallelogram ABCD can be found by calculating area of two triangles ABD and triangle BCD. In $\Delta$ADB , $Sin\theta = \cfrac{P_1}{AD}\;\Rightarrow AD=BC=\cfrac{P_1}{Sin\theta}$ $$ $$ In $\Delta$BCD , $Sin\theta =\cfrac{P_2}{DC}\;\Rightarrow DC=AB=\cfrac{P_2}{Sin\theta}$ $\therefore$ Area ABCD = $2.(\cfrac{1}{2}.AB.AD.Sin\theta)$ […]
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Angle bisector is locus of point $P(h,k)$ which move such that perpendicular distance of point from lines $L_1=0$ and $L_2=0$ are equal. If the lines $L_1\,:\,a_1x+b_1y+c_1=0$ and $L_2\,:\,a_2x+b_2y+c_2=0$ intersect at point $Q$ i.e $\vert \cfrac{a_1h+b_1k+c_1}{\sqrt{a_1^2+b_1^2}} \vert = \vert \cfrac{a_2h+b_2k+c_2}{\sqrt{a_2^2+b_2^2}} \vert$ Now Replace $(h,k)\rightarrow (x,y)$ we get bisectors $B_1=0\;,\;B_2=0$. $$\Rightarrow \Bigl( \cfrac{a_1x+b_1y+c_1}{\sqrt{a_1^2+b_1^2}}\Bigr)=\pm \Bigl( \cfrac{a_2x+b_2y+c_2}{\sqrt{a_2^2+b_2^2}}\Bigr) $$ Let […]
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Shortest distance of a point with respect to line is along the perpendicular to line
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Inclusion and Exclusion principle The principle of inclusion and exclusion is a counting technique in which the elements satisfy at least one of the different properties while counting elements satisfying more than one property are counted exactly once. For example if we want to count number of numbers in first $100$ natural numbers which are either […]
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