Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of $$4~\mathop A\limits^o $$. The radius of sodium atom is __________ $$\times ~10^{-1}$$ $$\mathop A\limits^o $$ (Nearest integer)

Let a$$_1$$, a$$_2$$, a$$_3$$, .... be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3^rd and 5^th terms be $$\frac{1}{9}$$. Then $$6(a_2+a_4)(a_4+a_6)$$ is equal to

Let $$|\vec{a}|=2,|\vec{b}|=3$$ and the angle between the vectors $$\vec{a}$$ and $$\vec{b}$$ be $$\frac{\pi}{4}$$. Then $$|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^{2}$$ is equal to :

Let the centre of a circle C be $$(\alpha, \beta)$$ and its radius $$r < 8$$. Let $$3 x+4 y=24$$ and $$3 x-4 y=32$$ be two tangents and $$4 x+3 y=1$$ be a normal to C. Then $$(\alpha-\beta+r)$$ is equal to :