Given, $(a, b)$ belongs to relation $R$ if $gcd(a, b) = 1$, $2a \neq b$.
Here $gcd$ means greatest common divisor. $gcd$ of two numbers is the largest number that divides both of them.

(1) For Reflexive,
In $aRa$, $gcd(a, a) = a$. Therefore, this relation is not reflexive.

(2) For Symmetric:
Take $a = 2, b = 1 \Rightarrow gcd(2, 1) = 1$. Also $2a = 4 \neq b$.
Now $gcd(b, a) = 1 \Rightarrow gcd(1, 2) = 1$ and $2b$ should not be equal to $a$.
But here, $2b = 2 = a \Rightarrow R$ is not Symmetric.

(3) For Transitive:
Let $a = 14, b = 19, c = 21$
$gcd(a, b) = 1, 2a \neq b$
$gcd(b, c) = 1, 2b \neq c$
$gcd(a, c) = 7, 2a \neq c$
Hence not transitive. $\Rightarrow R$ is neither symmetric nor transitive.