For the relation $R = \{(a, b): a \leq b\}$ in $\mathbb{R}$, which of the following is correct?

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

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :

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The function $f: [0, \infty) \rightarrow \mathbb{R}$ defined by, $f(x) = 2x^2 + 3$, is

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = [x]$, where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?

(A) f is one-one but not onto

(B) f is not onto

(C) f is not one-one

(D) f is one-one and onto

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The number of all onto functions from the set {1, 2, .......n} to itself is

Which of the following statements are true?

(A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto.

(B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto.

(C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto.

(D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto.

(Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers)

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