Application of ...

The values of $$x$$ satisfying $$\left| sinx \right| ^{\left| cosx \right|} +log_\left| cosx \right| \left| sinx \right| =2,$$ where $$x\epsilon (0,\dfrac{\pi}{2}),$$ is  

The slope of the straight line which is both tangent and normal to the curve $$4x^3=27y^2$$ is 

The function $$f(x)=log x$$

Let $$g(x)=\displaystyle \int _{1-x}^{1+x}t|f'(t)|dt$$, where $$f(x)$$ does not behave like a constant function in any interval $$(a,b)$$ and the graph of $$y=f'(x)$$ is symmetric about the line $$x=1$$, then

Three normals are drawn from the point $$\left(c,0\right)$$ to the curve $${y}^{2}=x.$$If two of the normals are perpendicular to each other,then $$c=$$

The function $$f(x)=\dfrac{x}{x^2+1}$$ increasing, if 

The approximate value of $$\sqrt[10]{0.999}$$ is 

If the line $$x+y=0$$ touches the curve $$2y^2=\alpha x^2+\beta $$ at $$(1,-1),$$ then $$(\alpha ,\beta )=$$

Let $$f ( x ) = \frac { \csc x + \cot x - 1 } { 1 + \cot x - \csc x }$$. The primitive of $$f ( x )$$ with respect to $$x$$ is equal to (Where $$C$$ is constant of integration.)

Let A = {1, 2, ......... 10} and B = {1, 2, .......... 5}
f : A $$\rightarrow$$ B is a non-decreasing into function, then number of such function is