A uniform square plate has a small piece \(Q\) of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The moment of inertia about the \(\mathrm{z}\)-axis is then,

1. increased
2. decreased
3. the same
4. changed in manner

With reference to the figure of a cube of edge a and mass m, the following statements are given. (O is the centre of the cube).

(a) The moment of inertia of the cube about the z-axis is ${\mathrm{I}}_{\mathrm{z}}={\mathrm{I}}_{\mathrm{x}}+{\mathrm{I}}_{\mathrm{y}}$
(b) The moment of inertia of cube about z'-axis is ${\mathrm{I}}_{\mathrm{z}}\text{'}={\mathrm{I}}_{\mathrm{z}}+\frac{{\mathrm{ma}}^2}{2}$
(c) The moment of inertia of cube about z"-axis is $={\mathrm{I}}_{\mathrm{z}}+\frac{{\mathrm{ma}}^2}{2}$
(d) ${\mathrm{I}}_{\mathrm{x}} = {\mathrm{I}}_{\mathrm{y}}$

Choose the correct statements:

1. (a, c)
2. (a, d)
3. (b, d)
4. (b, c)