If `|z| geq3`, then

If z is a complex number such that |z|geq2 , then the minimum value of |z+1/2|

Match the column Column-I Column-II a. If ||x-1|-2|geq3, then x in p. [-2,-1]uu[5,6] b. If ||x-1|-2|lt=3,t h e nx in q. [-4,6] c. If 2 lt= |x-3|lt=3,t h e nx in r. (-oo,-4]uu[6,oo) d. If 2lt=||x-3|-1|lt=3,t h e nx in s. [0,1]uu[5,6]

If x,y,z gt 0 then prove that (x+y+z)(1/x+1/y+1/z) geq 9

Statement 1: If x ,y ,z are the sides of a triangle such that x+y+z=1,t h e n((2x-1+2y-1+2z-1)/3)geq((2x-1)(2y-1)(2z-1))^(1//3)dot Statement 2: For positive numbers AdotMdotgeqGdotMdotgeqHdotMdot

Let a=3^(1/(223))+1 and for all n geq3,l e tf(n)=^n C_0dota^(n-1)-^n C_1dota^(n-2)+^n C_2dota^(n-3)-+(-1)^(n-1).^n C_(n-1) a^0 . If the value of f(2007)+f(2008)=3^k where k in N , then the value of k is.

If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq3//2.

If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq3//2.

If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq3//2.

Let z=x+i y be a complex number, where xa n dy are real numbers. Let Aa n dB be the sets defined by A={z :|z|lt=2}a n dB={z :(1-i)z+(1+i)bar z geq4} . Find the area of region AnnB

Let z=x+i y be a complex number, where xa n dy are real numbers. Let Aa n dB be the sets defined by A={z :|z|lt=2}a n dB={z :(1-i)z+(1+i)bar z geq4} . Find the area of region AnnB