What are the answers to the following geometry problems regarding quadrilaterals, cuboids, and cubes?

Here are the solutions to the questions:

1. The quadrilateral whose diagonals bisect the vertex through which they pass is

• In a square, the diagonals bisect the angles at the vertices (each angle is 90 degrees, and the diagonal divides it into two 45-degree angles).
• Answer: b) Square

2. The figure that is not a parallelogram is

• A parallelogram is a quadrilateral with two pairs of parallel sides.
• A square is a parallelogram.
• A rhombus is a parallelogram.
• A trapezium (or trapezoid) has only one pair of parallel sides, so it is not a parallelogram.
• Answer: b) Trapezium

3. The length of the longest rod that can fit in a cuboidal box of dimensions $a \times b \times c$ is

• The longest rod that can fit in a cuboidal box is its space diagonal. The formula for the space diagonal of a cuboid with dimensions $a, b, c$ is $\sqrt{a^2+b^2+c^2}$.
• Answer: b) $\boxed{\sqrt{a^2+b^2+c^2}}$

4. Three cubes of edges $x$ cm, 4 cm and 5 cm are melted and shaped into a large cube of edge 6 cm. Then the value of $x$ is