Solution:
Option A : {x:x∈N and x2<36}
As we can see that, elements of {x:x∈N and x2<36} are: 1,2,3,4,5
So, there are 5 elements in the set {x:x∈N and x2<36}
Hence, the set {x:x∈N and x2<36} is not a singleton set.
Option B: {x∈z:0<x<10}
As we can see that, elements of {x ∈ z: 0 < x < 10} are: 1, 2, 3, ........, 9
So, there are 9 elements in the set {x ∈ z: 0 < x < 10}
Hence, the set {x ∈ z: 0 < x < 10} is not a singleton set
OptionC: {x:x∈N and x2=x}
∵ x2=x
⇒x2−x=0
⇒ x (x - 1) = 0
⇒ x = 0 or 1
But since x ∈ N. So, x = 0 ∉ {x: x ∈ N and x2 = x}
So, only x = 1 ∈ {x: x ∈ N and x2 = x}
Hence, {x: x ∈ N and x2 = x} is a singleton set
Option D: {x ∈ N: x is even}
As we can see that, elements of {x ∈ N: x is even} are: 2, 4, 6, 8, ........
So, there are infinitely many elements in the set {x ∈ N: x is even}
Hence, {x ∈ N: x is even} is not a singleton set
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