Which of the following 3D polyhedra satisfy Euler's formula V - E + $F = 2$?
Each listed solid is a convex polyhedron and satisfies V-E+F=2: cube 8-12+6, tetrahedron 4-6+4, triangular prism 6-9+5, and square pyramid 5-8+5.
A 2D shape has rotational symmetry of order 4 and 4 lines of reflectional symmetry. What is the shape?
A square has 4 lines of symmetry and 90-degree rotational symmetry (order 4).
Find the order of rotational symmetry for a regular hexagon.
A regular hexagon maps onto itself 6 times during a full 360-degree turn (every 60 degrees). Order = 6.
What is the mirror image of the word 'GATE' when a vertical plane mirror is placed to its right?
A vertical mirror reverses the order of characters from right to left and horizontally flips each individual character.
In a water-image (horizontal mirror) reflection, which change occurs?
A horizontal mirror produces a water image: vertical positions are reversed, while the left-right order is retained.