List of top Mathematics Questions on Relations and functions asked in UP Board XII

Prove that the function \( f : \mathbb{R} \to \mathbb{R}^+ \) defined by \( f(x) = e^x \) is one-one.
If \( A = \{a, b, c\} \) and \( B = \{1, 2\} \), then find the number of relations from \( A \) to \( B \).
A relation $R = \{(a, b) : a = b - 1, b > 4\}$ is defined on set $\mathbb{N}$, then correct answer will be:
Prove that a one-one function \( f : \{2, 3, 4\} \to \{2, 3, 4\} \) is onto.
If $f: X \rightarrow Y$ is an onto function, if and only if the range of $f$ will be:
Prove that in the set $\mathbb{Z}$ of integers the relation $R$ given by $R = \{(a,b): 5 \text{ divides } (a-b)\}$ is an equivalence relation.
The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x^{2} + 5$ will be:
In the set $\{1, 2, 3, 4, 5, 6\}$, the relation $R$ defined by $R = \{(a, b) : b = a+1\}$ will be:
Prove that the relation $R = \{(a,b) \in \mathbb{Z} \times \mathbb{Z} \;|\; (a-b)$ is divisible by $2\}$ is an equivalence relation.
The modulus function $f: \mathbb{R} \to \mathbb{R}^{+}$ given by $f(x) = |x|$ will be: