IBPS PO Quantitative Aptitude: Geometry questions with solutions

Q1. Find the length of BC. Given that \(\angle CDB = \angle DAB = 90^\circ\), \(AD = 6\), and \(DC = 8\).

1. 24
2. 26
3. 22
4. 28

Answer: 24

Since \(\angle CDB\) and \(\angle DAB\) are right angles, the figure forms right triangles that can be related using Pythagoras and similarity. Using the given lengths \(AD=6\) and \(DC=8\), the required side comes out to be 24.

Q2. Which shape has no sides?

1. rectangle
2. triangle
3. circle
4. square

Answer: circle

A circle is a curved figure and has no sides or vertices. The other options are polygons with straight sides.

Q3. Perimeter of a right angled triangle is 60m and length of hypotenuse of right angled triangle is 25m. If base of the right angled triangle is the smallest side, then find length of smallest side.

1. 10m
2. 15m
3. 21m
4. 25m

Answer: 15m

a+b=60-25=35. a²+b²=25²=625. (a+b)²=1225=625+2ab → ab=300. (b-a)²=(a+b)²-4ab=25 → b-a=5. Solving a+b=35, b-a=5 gives b=20, a=15. Smallest side=15m.