A rhombus is formed by joining the midpoints of the sides of a unit square.

What is the diameter of the largest circle that can be inscribed within the rhombus?

An equilateral triangle, a square and a circle have equal areas.

What is the ratio of the perimeters of the equilateral triangle to square to circle?

Given below are three conclusions drawn based on the following three statements.

Statement 1 : All teachers are professors.

Statement 2 : No professor is a male.

Statement 3 : Some males are engineers.

Conclusion I : No engineer is a professor.

Conclusion II : Some engineers are professors.

Conclusion III : No male is a teacher.

Which one of the following options can be logically inferred?

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?