The relation $R=\left\{(a, b): a \leq b^2\right\}$ on the set of real numbers is:

Neither reflexive nor symmetric

$R=\left\{(a, b): a \leq b^2\right\}$

→ this is not reflexive

for eg: $a=\frac{1}{2}~~~b^2=\frac{1}{4}=a^2$

here a > b → false lies R

→ NOT REFLEXIVE

→ this is not symmetric

for eg: a = 2,  b = 5

$a^2 = 4, ~~b^2=25$

so a ≤ b holds true

b ≤ a (doesn't hold true)

→ Not symmetric

→ this is not transitive

e.g: a = 2,  b = -2,  c = -1

$a^2 = 4, ~~b^2=4,~~c^2=1$

$a \leq b^2 \Rightarrow(a, b) \in R$

$b \leq c^2 \Rightarrow(b, c) \in R$

but  $a>c \Rightarrow(a, c) \notin R$

→ Not transitive

Option → 2 - Neither reflexive nor symmetric