Relations and Functions
Showing all questions for Class JEE Math
Question 1:
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements
(S1): The number of elements in R is 18, and
(S2): The relation R is symmetric but neither reflexive nor tr...
Question 2:
Let
\[
A = \{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R} : |\alpha - 1| \leq 4 \;\;\text{and}\;\; |\beta - 5| \leq 6\}
\]
and
\[
B = \{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R} : 16(\alpha - 2)^2 + 9(\beta - 6)^2 \leq 144\}.
\]
...
Question 3:
Let
\[
A = \{-3, -2, -1, 0, 1, 2, 3\}
\]
and \(R\) be a relation on \(A\) defined by
\[
x R y \;\;\text{if and only if}\;\; 2x - y \in \{0,1\}.
\]
Let \(l\) be the number of elements in \(R\). Let \(m\) and \(n\) be the minimum number of elements re...
Question 4:
Consider the sets
\[
A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + y^2 = 25\}, \quad
B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + 9y^2 = 144\},
\]
\[
C = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : x^2 + y^2 \leq 4\}, \quad
D = A ...
Question 5:
Let \(A = \{-2,-1,0,1,2,3\}\). Let \(R\) be a relation on \(A\) defined by
\[
x \,R\, y \iff y = \max\{x,1\}.
\]
Let \(l\) be the number of elements in \(R\). Let \(m\) and \(n\) be the minimum number of elements required to be added in \(R\) to mak...
Question 6:
Let \(A = \{-3,-2,-1,0,1,2,3\}\). Let \(R\) be a relation on \(A\) defined by
\[
x \,R\, y \iff 0 \leq x^2 + 2y \leq 4.
\]
Let \(l\) be the number of elements in \(R\) and \(m\) be the minimum number of elements required to be added in \(R\) to make...
Question 7:
Let \(A=\{1,2,3, \ldots ., 100\}\) and \(R\) be a relation on \(A\) such that \(R=\{(a, b): a=2 b+1\}\).
Let \((a_1,\,a_2),(a_2,\,a_3),(a_3,\,a_4), \ldots .,(a_k,\,a_{k+1})\)
be a sequence of \(k\) elements of \(R\) such that the second entry of...