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
The sum of the coefficients of three consecutive terms in the binomial expansion of $$(1+\mathrm{x})^{\mathrm{n}+2}$$, which are in the ratio $$1: 3: 5$$, is equal to :