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: find value of x : ( 422 + 404 ) ^ 2 − ( 4 × 422 × 404 ) = x . 
Options: a ) 234 , b ) 267 , c ) 324 , d ) 356 , e ) 577
c

Problem: gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ? 
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
b

Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 4 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ? 
Options: a ) 36 , b ) 41 , c ) 38 , d ) 40 , e ) 42

b