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: the ration of the father ' s age to his son ' s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :
Options: a ) 5 : 2 , b ) 2 : 1 , c ) 11 : 7 , d ) 13 : 9 , e ) none of these
b

Problem: if 7 ^ k = 2 , then 7 ^ ( 4 k + 2 ) =
Options: a ) 729 , b ) 754 , c ) 784 , d ) 783 , e ) 108
c

Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24
a