$$\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2} \cdot \mathrm{XH}_{2} \mathrm{O}$$ and $$\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \cdot \mathrm{YH}_{2} \mathrm{O}$$, represent formula of the crystalline forms of nitrate salts. Sum of $$\mathrm{X}$$ and $$\mathrm{Y}$$ is _____________.
The volume of hydrogen liberated at STP by treating $$2.4 \mathrm{~g}$$ of magnesium with excess of hydrochloric acid is _________ $$\times ~10^{-2} \mathrm{~L}$$
Given : Molar volume of gas is $$22.4 \mathrm{~L}$$ at STP.
Molar mass of magnesium is $$24 \mathrm{~g} \mathrm{~mol}^{-1}$$
If the radius of the largest circle with centre (2,0) inscribed in the ellipse $$x^2+4y^2=36$$ is r, then 12r$$^2$$ is equal to :
Let $$a, b, c$$ and $$d$$ be positive real numbers such that $$a+b+c+d=11$$. If the maximum value of $$a^{5} b^{3} c^{2} d$$ is $$3750 \beta$$, then the value of $$\beta$$ is