JEE Main Math Class 11 Relations and Functions Part 1 Questions

Here, R1={(x,y)∈N×N:2x+y=10} and
R2={(x,y)∈N×N:x+2y=10}
For R1;2x+y=10 and x,y∈N
So, possible values for x and y are:
x=1,y=8 i.e. (1,8);
x=2,y=6 i.e. (2,6);
x=3,y=4 i.e. (3,4) and x=4,y=2 i.e. (4,2).
R1={(1,8),(2,6),(3,4),(4,2)}
Therefore, Range of R1 is {2,4,6,8}
R1 is not symmetric
Also, R1 is not transitive because (3,4),(4,2)∈R1 but (3,2)∉R1
Thus, options A,B and D are incorrect.
For R2;x+2y=10 and x,y∈N
So, possible values for x and y are:x=8,y=1 i.e. (8,1);
x=6,y=2 i.e. (6,2);
x=4,y=3 i.e. (4,3) and
x=2,y=4 i.e. (2,4)
R2={(8,1),(6,2),(4,3),(2,4)}
Therefore, Range of R2 is {1,2,3,4}
R2 is not symmetric and transitive.