Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is ___________ $$\times$$ 10^$$-$$1 g. (in nearest integer)

Let $$f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$$, $$x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$$. Then, f is :

Let S_n be the sum of the first n terms of an arithmetic progression. If S_3n = 3S_2n, then the value of $${{{S_{4n}}} \over {{S_{2n}}}}$$ is :

The locus of the centroid of the triangle formed by any point P on the hyperbola $$16{x^2} - 9{y^2} + 32x + 36y - 164 = 0$$, and its foci is :