OA must be wrong ..it has to be B

no E is Correct because they are asking whether the (r,s) is on the line they say that the points x,y are on the space R as per the below statement


region R consists of all the points(x,y)

hence as the boundaries of the region are not specified we cannot say whether the point is there in Region R or not

Please correct me if I am wrong

Your answer "E" is correct but reasoning is __incorrect__.

The region R is nothing but an area which has all the points lying on the line 2x + 3y = 6. Now the line 3r + 2s = 6 (or for that matter 3x + 2y = 6) intersects the former line at exactly one point and that point is not (3,2). (You solve for x and y to find out the point of intersection).

So the answer is E.

In the XY-plan, region R consists of all the points(x,y) such that 2x+3y=6. Is the point (r,s) in region R?

this means that the region is nothing but the line 2x+3y =6 i.e all points that lie on this line

1) 3r+2s=6

this will also form a line which intersects the line 2x+3y at one pt so r,s may be on the line 2x+3y or it may not be one the line

INSUFF

2) r=3 and s=2

here we are given an exact coordinate location for the point r,s

i.e r =3 & s =2, now clearly this point does't lie on the line 2x+3y =6

so this is SUFF we knoe that the pt doesn't lie on the line coz it does not satisfy the equation of the line.

Now for this to be INSUFF we need to prove that

3,2 lies on the line 2x+3y =6 or it does not lie on the line

now since the coordinates of the pt are constant (not changing) how can the point first lie on the line & not lie on it, this is possible only if the pt is variable (coordinates) or the region itself is changing to sum up there has to be some variation/change to prove this is INSUFF which IMO is not possible here.

so the ans should be B

BTW is this question from a credible source?