List of top General Aptitude Questions on Geometry

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?

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:


 

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:

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)?

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.


 

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.

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:
\includegraphics[width=0.5\linewidth]{8.png}
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 \( R \)?
\includegraphics[width=0.5\linewidth]{4.png}
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.
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:
\includegraphics[width=0.5\linewidth]{8.png}
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 \( R \)?
\includegraphics[width=0.5\linewidth]{4.png}
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.
A \(100\text{ cm} \times 32\text{ cm}\) rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions \(100\text{ cm} \times 1\text{ cm}\).
The total number of creases visible when the sheet is unfolded is __________.