List of top General Aptitude Questions on Geometry asked in GATE CY, GATE CE

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:


 

A rectangle has a length \(L\) and a width \(W\), where \(L>W\). If the width, \(W\), is increased by 10%, which one of the following statements is correct for all values of \(L\) and \(W\)? 
Select the most appropriate option to complete the above sentence.

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?

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72º anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. Moves forward by 10 cm.
2. Turns 144º clockwise.
The pattern made by the trace left behind by the ant is:

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?

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above. The value of \( \theta \), in degrees, is