Values of $$c$$ as per Rolle's theorem for $$f(x)=\sin x+\cos x+6$$ on $$[0,2 \pi]$$ are

A poster is to be printed on a rectangular sheet of paper of area $$18 \mathrm{~m}^2$$. The margins at the top and bottom of $$75 \mathrm{~cm}$$ each and at the sides $$50 \mathrm{~cm}$$ each are to be left. Then the dimensions i.e. height and breadth of the sheet, so that the space available for printing is maximum, are ________ respectively.

The equation of the normal to the curve $$3 x^2-y^2=8$$, which is parallel to the line $$x+3 y=10$$, is

If the curves $$y^2=6 x$$ and $$9 x^2+b y^2=16$$ intersect each other at right angle, then value of '$$b$$' is