maths for net

1..discuss the nature of solution;
a..dy/dx=sin(xy) , y(0)=3
b..xdy/dx=y+2 x*2 , y(o)=o
c..dy/dx=x*2+y*2 , Y(0)=0
d..2xdy/dx=3(2y-1) , y(0)=1/2
2...which can not be cardinality of a field 4 ,6, 7, 27.
3...which one is correct..
a..a computer can be used to sort out 10 lakh number in increasing order.
b..a computer can be used for factoring any integer.
4...which one is correct
a..every principal ideal domain is euclidean domain.
b..the groups of units in the ring Z/37Z is cyclic.
5..which one is software.word perfect,internet explorer, nt, lotous
6..in a non -abelian group , the element a has a order 108, the order of a * 42 is....
7..in a permutation group S6, THE NUMBER OF ELEMENTS conjugate to (123)(456) is...