For the functions $f(x) = x^2$ and $g(x) = x^3$, which of the following statements are TRUE?

[where N is the set of natural numbers and Z is the set of integers]

(A) $f: N \to N$ is one-one but not onto.

(B) $f: Z \to Z$ is neither one-one nor onto.

(C) $g: N \to N$ is one-one but not onto.

(D) $g: Z \to Z$ is one-one but not onto.

Choose the correct answer from the options given below:

The domain of the function $y = \sin^{-1}(x-1) + \cos^{-1}\sqrt{x-1}$ is:

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$, then R is

The Relation $R = \{(x, y) : x \leq y^2\}$ defined on the set $\mathbf{R}$ of Real numbers is :

(A) reflexive but not symmetric

(B) neither reflexive nor symmetric

(C) neither reflexive nor transitive

(D) reflexive but not transitive

(E) not reflexive but symmetric

Choose the correct answer from the options given below :

If R be a relation on the set of integers Z, given by R = {(a, b) : (a - b) is a multiple of 3}, then R is:

Let R be a relation on the set of natural numbers N defined by nRm if n divides m. Then R is :

(A) Reflexive Relation

(B) Symmetric Relation

(C) Transitive Relation

(D) Identity Relation

Choose the correct answer from the options given below :

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