A kite is $$120 \mathrm{~m}$$ high and $$130 \mathrm{~m}$$ of string is out. If the kite is moving away horizontally at the rate of $$39 \mathrm{~m} / \mathrm{sec}$$, then the rate at which the string is being out, is

If slope of a tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then a - b is

The equation $$x^3+x-1=0$$ has

The range of values of $$x$$ for which $$f(x)=x^3+6 x^2-36 x+7$$ is increasing in