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: in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ? 
Options: ['a ) 15 ohms', 'b ) 15 / 8 ohms', 'c ) 1 / 8 ohms', 'd ) 8 / 15 ohms', 'e ) 8 ohms']

SOLUTION: b

PROBLEM: Problem: two cubes of their volumes in the ratio 343 : 729 . the ratio of their surface area is : 
Options: a ) 7 : 9 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5

SOLUTION: a

PROBLEM: Problem: two equilateral triangles of side 12 cm are placed one on top of another , such that a 6 pointed star is formed . if the six verticals lie on a circle what is the area of the circle not enclosed by the star ? 
Options: ['a ) 68', 'b ) 83', 'c ) 57', 'd ) 61', 'e ) 62']

SOLUTION:
a