List of top Mathematics Questions on Relations and Functions asked in JEE Main

Let \( A = \{0,1,2,\ldots,9\} \). Let \( R \) be a relation on \( A \) defined by \((x,y) \in R\) if and only if \( |x - y| \) is a multiple of \(3\). Given below are two statements:
Statement I: \( n(R) = 36 \).
Statement II: \( R \) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.

Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions \( f : A \to B \) is equal to
The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:
Let \( A = \{1,2,3,\ldots,9\} \) and \( R \subset A \times A \) be defined by \[ (x,y) \in R \iff |x-y| \text{ is a multiple of } 3. \] Consider the following statements:
S\(_1\): Number of elements in \( R \) is 36.
S\(_2\): \( R \) is an equivalence relation.
Which of the following is correct?
Let the sets \[ A = \{x : |x - 3| - 3 \le 1,\; x \in \mathbb{Z}\} \] \[ B = \left\{ x : x \in \mathbb{R},\; x \ne 1,2,\; \frac{(x-2)(x-4)}{(x-1)} \log_e |x-2| = 0 \right\} \] Then the number of onto functions from \( A \) to \( B \) is:
If the domain of the function \[ f(x)=\frac{1}{\ln(10-x)}+\sin^{-1}\!\left(\frac{x+2}{2x+3}\right) \] is \[ (-\infty,-a]\ \cup\ (-1,b)\ \cup\ (b,c), \] then find the value of \( (b+c+3a) \).
Let \( M = \{1,2,3,\ldots,16\} \) and \( R \) be a relation on \( M \) defined by \( xRy \) if and only if \( 4y = 5x - 3 \). Then, the number of ordered pairs required to be added to \( R \) to make it symmetric is