Differentiation...

If $$y=y(x)$$ and it follows the relation $$e^{xy^{2}}+y\cos(x^{2})=5$$ then $$y'(0)$$ is equal to

If $$y=a\ \sin\ x+b\ \cos\ x$$, then $$y^{2}+\left ( \dfrac{dy}{dx} \right )^{2}$$ is

The total number of ways of arranging the letters $$AAABBBCCDEF$$ in a row such that letters $$C$$ are separated from one another is

The maximum number of points of intersection of $$7$$ staright lines and $$5$$ circles when $$3$$ straight lines are parallel and $$2$$ circles are concentric,is /are

Choose the odd one out . 

If $$f(x+y)=2f(x).f(y)$$ for all $$x,y$$, where $$f'(0)=3$$ and $$f'(4)=2$$ then $$f'(4)=3$$ is equal to

In how many ways atleast one horse and atleast one dog can be selected out of eight horses and seven dogs.

If y = sin $$^{-1} (x. \sqrt{1-x}+ \sqrt{x}\sqrt{1-x^2})$$, then $$\dfrac{dy}{dx} =$$

If $$64a^2+36b^2=400, ab=4 $$ , then $$8a+6b$$ is: 

The number of positive integral solutions of the equation $$x _ { 1 } x _ { 2 } x _ { 3 } x _ { 4 } x _ { 5 } = 1050$$ is