Differentiation...

A Printer number the pages of a book starting with $$1$$ and used $$3193$$ digit in all. How many pages does the book have:

The number of permutations of letters of the word "PARALLAL" atken four at a time must be, 

If $$(\cos x)^{y}=(\sin y)^{x}$$, then $$\dfrac{dy}{dx}=$$

7, 11, 23, 51, 103 ?

Using all digits $$2,3,4,5,6$$ how many even number can be formed 

13, 16, 22, 33, 51 ?

655, 439, 314, 250, 223 ?

If $$y = \exp \left\{ {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + ....} \right\}$$ then $$\frac {dy}{dx}=$$

The differential of $$f(x)=\sqrt{\dfrac{2-x}{2+x}}$$ at $$x=0$$ and $$\delta x=0.15$$ is

Six people are going to sit in a row on a bench. $$A$$ and $$B$$ are adjacent, $$C$$ does not want to sit adjacent to $$D.E$$ and $$F$$ can sit anywhere. Number of ways in which these six people can be seated is