Write the value of `a r g(z)+a r g( bar(z) )` .

If |z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)+ z_(2)z_(3)|= 12 , then find the value of |z_(1) + z_(2) + z_(3)| .

If f:R -> R, g:R -> R defined as f(x) = sin x and g(x) = x^2 , then find the value of (gof)(x) and (fog)(x) and also prove that gof != fog .

In the given figure three lines bar(AB) , bar(CD) and bar(EF) intersecting at O. Find the values of x, y and z it is being given that x : y : z = 2 : 3 : 5

The value of (z+3)(bar(z)+3) is equivalent to

If f:R rarr R and g : R rarr R are defined by f(x) = 3x + 2 and g(x) = x^2 - 3 , then the value of x such that g(f(x))=4 are

If f: (R) rarr (R) and g (R) rarr (R) defined by f(x)=2x+3 and g(x)=x^(2)+7 ,then the values of x such that g(f(x))=8 are

Calculate Delta_(r )G^(@) for the reaction for which the value of K_(p) is 1.5 xx 10^(10) at 300 K.

If z^(2)+z+1=0 , where z is a complex number, then the value of (z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(3)))^(2)+....+(z^(6)+(1)/(z^(6)))^(2) is

If f: R rarr R and g:R rarr R are one-to-one, real valued functions, then the value of the integral int_(-pi)^(pi) [f(x)+f(-x)][g(x)-g(-x)]dx =

If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) (sqrt(pi))/(2) "and (gof)"((pi)/(3)) .