Q1: A vertical column has two moments of inertia (i.e. I_xx and I_yy ). The column will tend to buckle in the direction of the

ANS:D - minimum moment of inertia

Buckling:

Sudden failure of column in lateral direction is called Buckling. It occurs when the Euler's critical load (n*pi^2*E*I)/L^2 is less than allowable compression load.

Moment of inertia.
Tendency to resist angular acceleration.

So from above two definition it is clear that when moment of inertia is low , then the column is more vulnerable to buckling as it couldn't resist much of lateral movement.