1)consider Z24 as additive group modulo 24.Then find the number of element of order 8 in group 24 ?

2)Consider Z5 and Z20 as ring modulo 5 and 20.Them the number of homomorphisms

p:Z5-->Z20 is?

3)if Q is a field of rational numbers and Z2 as a field of modulo 2 let

f(x)=x^3-9x^2+9x+3 then witch of following is correct.1)f(x) is irreducible over Z2

2)f(x) is irreducible over both Q and Z2

3)f(x) is reducible over Q but irreducible and Z2

4)f(x) is reducible over both Z2 and Q

please explain with detail.Thanks in advance

(these questions asked by indian institue of technology delhi asked in gate test )