Geometry - General Aptitude (GA) Previous Year Questions

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?

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?

In the given figure, \( P \), \( Q \), and \( R \) are three points on a circle of radius 10 cm with \( O \) as its center, \( PQ = RQ \), and \( \angle PQR = 45^\circ \). The figure is representative. The area of the shaded region \( PQRO \) is __________ cm².

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:
Note: The figure shown is representative.