In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

[EX Q]: Problem: 36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options: ['a ) 11', 'b ) 12', 'c ) 13', 'd ) 15', 'e ) 18']
[EX A]: b

[EX Q]: 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 100,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
[EX A]: d

[EX Q]: Problem: the diagonal of a rhombus are 80 m and 120 m . its area is :
Options: a ) 4500 , b ) 4000 , c ) 4800 , d ) 4600 , e ) 4320
[EX A]:
c