TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6

SOLUTION: b

PROBLEM: Problem: the area of a square is 4225 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square . 
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 41 : 130

SOLUTION: e

PROBLEM: Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) 
Options: ['a ) 22.78', 'b ) 23.54', 'c ) 24.5', 'd ) 25.55', 'e ) 23.51']

SOLUTION:
a