CBSE Class 12 · 2015 · Relations And Functions XIILong Answer

Reflexive: for $(a,b)$, check $(a,b)R(a,b)$, i.e. $ab(b+a)=ba(a+b)$, which is identically true. So $R$ is reflexive.
Symmetric: suppose $(a,b)R(c,d)$, so $ad(b+c)=bc(a+d)$. Dividing by $abcd$ gives the symmetric form

which is precisely the condition $cb(d+a)=da(c+b)$, i.e. $(c,d)R(a,b)$. So $R$ is symmetric.
Transitive: let $(a,b)R(c,d)$ and $(c,d)R(e,f)$. In the divided form these read

Adding and cancelling $\frac{1}{c}+\frac{1}{d}$ from both sides gives $\frac{1}{b}+\frac{1}{e}=\frac{1}{a}+\frac{1}{f}$, i.e. $af(b+e)=be(a+f)$, so $(a,b)R(e,f)$.