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

Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between : 
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
c

Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 580 ? 
Options: a ) rs . 500 , b ) rs . 5100 , c ) rs . 530 , d ) rs . 540 , e ) none of these
a

Problem: rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is 
Options: a ) rs 429 , b ) rs 412 , c ) rs 400 , d ) rs 129 , e ) rs 122

c