Co-ordinate Geonetry Calculus Trignometry Algebra for IITJEE Quadratic Equations Permutation And Combination Complex Number Modulus Quadratic Equations. (1) Condition for roots of quadratic equation. (2) Solution of Quadratic Equation. (3) For relation between coefficients and zeros of polynomial ( Video Link Only ) Permutation And Combination. PERMUTATION WITH RESTRICTION. Distribution of distinct Objects. Distribution of Identical objects into Distinct Groups. Principle of Inclusion and Exclusion . Complex Numbers. (1) How to find Argument of a complex number. ( Video Link Only ) (2) Modulus of complex number and properties of modulus. (Video Link Only ) (3) Conjugate of Complex Number. ( Video Link Only ) Modulus. Modulus or Absolut value function. Read More Complex Number.-Discussion Forum$(Cos\theta +iSin\theta)^{2n+1}$ $$=\sum_{r=0}^{2n+1} {{2n+1}\choose r} Cos^{2n+1-r}\theta (i Sin\theta)^r$$ $\Rightarrow Cos(2n+1)\theta $ $$= \sum_{r=0}^{n} {{2n+1}\choose {2r} }Cos^{2n+1-2r}\theta (i Sin\theta)^{2r}$$ Permutation & CombinationFrom $^{(m-n)}P_r\,=\,30$ $$ $$ $(m-n)!=5.6.(m-n-r)!$ $\therefore m-n-r=4$ $$ $$ and $\, m-n=6\, ----(1)$ $$\therefore r=2$$ And $^{(m+n)}P_r\,=\,90$ TrignometryIn the equation LHS $\ge 1$ where as RHS $\le 1$ $$ $$ Hence LHS=RHS=1 is only possible solution. $\therefore x=2nπ\,,\forall n\in I$ for RHS = 1 and for same x LHS =1 if $a(2nπ)=mπ \,,m\in I$