The range of the function $f(x) = \frac{1}{3 - \sin 4x}$ is:

Let A = {1, 2, 3}. The number of equivalence relations containing (1, 3) is

Let X be a non-empty set and let P be the collection of all subsets of X. Let R be a relation in P, defined by $R = \{(A, B): A \text{ is subset of } B\}$. Then, R is

A. Reflexive relation

B. Symmetric relation

C. Not a transitive relation

D. Transitive relation

Choose the correct answer from the options given below:

A. A relation $R$ on a set $A$ is called an equivalence relation, if it is reflexive, symmetric and transitive.

B. The function $f : R \to R$ defined by $f(x) = e^x$ is not one-one.

C. The one-one function is also known as injective function.

D. The onto function is also known as subjective function.

E. A function $f : X \to Y$ is said to be many-one, if two or more than two elements in set $X$ have the different image in set $Y$.

Choose the correct answer from the option given below:

Let $R_1, R_2, R_3, R_4$ be the relations defined on the set $A=\{1,2,3\}$. then

Match List-I with List-II

Choose the correct answer from the options given below:

Which of the following functions from $\mathbb{Z}$ to $\mathbb{Z}$ is a bijective function? (where $\mathbb{Z}$ is set of integers)

Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is