Let A = $$\left[ {\matrix{ 2 & b & 1 \cr b & {{b^2} + 1} & b \cr 1 & b & 2 \cr } } \right]$$ where b > 0.

Then the minimum value of $${{\det \left( A \right)} \over b}$$ is -

On which of the following lines lies the point of intersection of the line,   $${{x - 4} \over 2} = {{y - 5} \over 2} = {{z - 3} \over 1}$$  and the plane, x + y + z = 2 ?

The value of $$\lambda $$ such that sum of the squares of the roots of the quadratic equation, x² + (3 – $$\lambda $$)x + 2 = $$\lambda $$ has the least value is -

The positive value of $$\lambda $$ for which the co-efficient of x² in the expression x² $${\left( {\sqrt x + {\lambda \over {{x^2}}}} \right)^{10}}$$ is 720, is -