When 10 mL of an aqueous solution of Fe²⁺ ions was titrated in the presence of dil H₂SO₄ using diphenylamine indicator, 15 mL of 0.02 M solution of K₂Cr₂O₇ was required to get the end point. The molarity of the solution containing Fe²⁺ ions is x $$\times$$ 10^$$-$$2 M. The value of x is __________. (Nearest integer)

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)

A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$ at the eye of the observer A while the angle of elevation of its center from the eye of A is 75$$^\circ$$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :

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 :