CAT 2023 Slot 1 – Geometry-Based Questions

1. The minor angle between the hour and minute hands of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8:48 am when this angle increases by 50% is:

A) 18 minutes
B) 20 minutes
C) 24 minutes
D) 30 minutes

2. A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals:

A) 4/3
B) 5/3
C) 8/5
D) 7/6

3. A circle has its center at (0, 0) and passes through the point (3, 4). What is the angle formed between the radius and the line passing through the center?

A) 30°
B) 45°
C) 60°
D) 90°

4. In a right-angle triangle, if the base is 6 units and height is 9 units, then the area of the triangle is:

A) 24 sq. units
B) 27 sq. units
C) 30 sq. units
D) 36 sq. units