Relations and F...

The real value of $$\theta $$for which the expression $$\dfrac { 1+icos\theta  }{ 1-2icos\theta  } $$ is a real number __________.

$$f(x)=4-(6-x)^{2/3}$$ in $$[5,7]$$

If $$S$$ is the set of all real $$x$$ such that $$\dfrac{2x}{2x^{2}+5x+2}>\dfrac{1}{x+1}$$, then $$S$$ is equal to

Let $$f(x)=x^{3}-2x+2$$. If real numbers $$a,b$$ and $$c$$ such that $$|f(a)|+|f(b)|+|f(c)|=0$$, then the value of $$f^{2}\left(a^{2}+\dfrac {2}{a}\right)+f^{2}\left(b^{2}+\dfrac {2}{b}\right)-f^{2}\left(c^{2}+\dfrac {2}{c}\right)$$ equal to

If $$\sqrt { \log _ { 4 } \left( \log _ { 2 } \left( \log _ { 2 } \left( x ^ { 2 } - 2 x + a \right) \right) \right. } )$$ is defined $$\forall x \in R$$, then

If $$f(x) = (x - 1)^{100} (x - 2)^{2(99)} (x - 3)^{3(98)} .... (x - 100)^{100}$$, then the value of $$ \dfrac{f' (101)}{f(101)}$$ is 

Let A be a finite set and n(A) = 5, then the number of relations which are not symmetric is _____________________.

Let $$y=x^{x+1}+\left(1+\dfrac{1}{x}\right)^{x}$$ then $$y'(1)$$ equal 

If $$f(x)=4x^{3}+3x^{2}+3x+4$$ , then $$x^{3}f(\frac{1}{x})$$ is equal to

If $$x\ \epsilon \ R$$, the number of solutions of $$\sqrt{2x+1}-\sqrt{2x-1}-1$$ is