Question

There have been two ways on making transuranium elements: neutron bombardment and
a)beta bombardment
b)gamma bombardment
c)positron bombardment
d)photon bombardment
e)heavy atom bombardment

Answer 1

there are actually three ways:
neutron bombardment
heavy metal bombardment
bombardment by deuterium and helium nuclei

http://oregonstate.edu/instruct/ch374/ch418518/Chapter%2015%20%20The%20Transuranium%20Elements-rev.pdf
See table 15-2 at the end. By the way, this document was written with one of the authors, Glen Seaborg, who on one of my talks at Georgia Tech, sat in my lecture (on teaching Chemistry). I shall never forget that honor.