List of top Mathematics Questions on Geometry asked in GATE AE

A rectangular paper sheet of dimensions \(54\text{ cm} \times 4\text{ cm}\) is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

A rectangular paper of \(20 \, \text{cm} \times 8 \, \text{cm}\) is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is:

Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?

In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\text{ cm}\), \(PT = 4\text{ cm}\) and \(PV = 5\text{ cm}\). What is the length of \(RS\) (in cm)? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}

A line of symmetry divides a figure into two parts that are mirror images. The given figure consists of 16 unit squares. Three are already black. What is the minimum number of additional squares that must be coloured black so that both \(PQ\) (vertical midline) and \(MN\) (diagonal) are lines of symmetry? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}