The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is _______ .

The value of $${\left( {0.16} \right)^{{{\log }_{2.5}}\left( {{1 \over 3} + {1 \over {{3^2}}} + ....to\,\infty } \right)}}$$ is equal to ______.

Let A = $$\left[ {\matrix{ x & 1 \cr 1 & 0 \cr } } \right]$$, x $$ \in $$ R and A⁴ = [a_ij].
If a₁₁ = 109, then a₂₂ is equal to _______ .

A bakelite beaker has volume capacity of 500 cc at 30^oC. When it is partially filled with Vm volume (at 30^oC) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $$\gamma $$_(beaker) = 6 × 10^{–6 o}C^–1 and $$\gamma $$_(mercury) = 1.5 × 10^{–4 o}C^–1, where $$\gamma $$ is the coefficient of volume expansion, then V_m (in cc) is close to ____.