Which statment is not true?

a)two lines lie in one plane and do not intersect if and only if the two lines are parallel.

b)if two lines are parallel, then they lie in one plane and do not intersect.

c)two lines lie in one plane if and only if the lines are parallel.

d)if two coplanar lines do not intersect, then the lines are parallel

Statement B and statement D are correct statements, so they can never be answered. 
Statement C is also an accurate statement, as parallel lines can not intersect and any two parallel lines decide a plane. [Rule for defining planes] 

So, Statement A is the only wrong statement in above options. 
Not only planar but, any two intersecting lines also decide a plane. 
That means intersecting lines can also be in one plane. 

Statement A is NOT TRUE in above statements.