List of top General Aptitude Questions on Geometry asked in GATE GG, GATE EY

In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii)?

Spheres of unit diameter are centered at \( (l, m, n) \), where \( l, m, \) and \( n \) take every possible integer value. The distance between two spheres is computed from the center of one sphere to the center of another sphere. For a given sphere, \( x \) is the distance to its nearest sphere and \( y \) is the distance to its next nearest sphere. The value of \( \frac{y}{x} \) is:
A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting, and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?

Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

A sphere of radius \(r\) cm is packed in a box of cubical shape. What should be the minimum volume (in cm\(^3\)) of the box that can enclose the sphere?
A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?
In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is
Two straight lines pass through the origin \( (x_0, y_0) = (0, 0) \). One of them passes through the point \( (x_1, y_1) = (1, 3) \) and the other passes through the point \( (x_2, y_2) = (1, 2) \). What is the area enclosed between the straight lines in the interval \( [0, 1] \) on the x-axis?

In the figure, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest shaded square is to be found. The outermost square has a side length of 10 cm.