JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{0,3,4,6,7,8,9,10\} \quad\) and \(R\) be the relation defined on A such that \(R =\{( x , y ) \in A \times A : x - y \quad\) is odd positive integer or \(x-y=2\}\). The minimum number of elements that must be added to the relation \(R\), so that it is a symmetric relation, is equal to \(...........\).
- A \(18\)
- B \(19\)
- C \(17\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(19\)
Step-by-step Solution
Detailed explanation
\(A =\{0,3,4,6,7,8,9,10\} \quad 3,7,9 \rightarrow \text { odd }\) \(R =\{ x - y =\text { odd }+ \text { ve or } x - y =2\} 0,4,6,8,10 \rightarrow \text { even }\) \({ }^3 C _1 \cdot{ }^5 C _1=15+(6,4),(8,6),(10,8),(9,7)\) \(Min ^{ m }\) ordered pairs to be added must be :…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(a>0, b>0\). Let \(e\) and \(\ell\) respectively be the eccentricity and length of the latus rectum of the hyperbola \(\frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1\). Let \(e ^{\prime}\) and \(\ell^{\prime}\) respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If \(e ^{2}=\frac{11}{14} \ell\) and \(\left( e ^{\prime}\right)^{2}=\frac{11}{8} \ell^{\prime}\), then the value of \(77 a+44 b\) is equal toJEE Mains 2022 Hard
- If the number of seven-digit numbers, such that the sum of their digits is even, is \(m \cdot n \cdot 10^{\mathrm{n}}\); \(m, n \in\{1,2,3, \ldots, 9\}\), then \(m+n\) is equal to _______JEE Mains 2025 Easy
- The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\), isJEE Mains 2023 Medium
- Let \(x=x(y)\) be the solution of the differential equation \(y^2 \mathrm{~d} x+\left(x-\frac{1}{y}\right) \mathrm{d} y=0\). If \(x(1)=1\), then \(x\left(\frac{1}{2}\right)\) is :JEE Mains 2025 Hard
- Let \(A=\left[a_{i j}\right]\) be a real matrix of order \(3 \times 3\), such that \(a_{i 1}+a_{i 2}+a_{i 3}=1\), for \(i=1,2,3\). Then, the sum of all the entries of the matrix \(A^{3}\) is equal to:JEE Mains 2021 Medium
- Let \(\vec a = 3\hat i + 2\hat j + x\hat k\) and \(\vec b = \hat i - \hat j + \hat k\), for some real \(x\). Then \(\left| {\vec a \times \vec b} \right| = r\) is possible ifJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(\vec a = 2\hat i + {\lambda _1}\hat j + 3\hat k\), \(\vec b = 4\hat i + \left( {3 - {\lambda _2}} \right)\hat j + 6\hat k\) \(\vec c = 3\hat i + 6\hat j + \left( {{\lambda _3} - 1} \right)\hat k\) be three vectors such that \(\vec b = 2\vec a\) and \(\vec a\) is perpendicular to \(\vec c\). Then a possible value of \(\left( {{\lambda _1},{\lambda _2},{\lambda _3}} \right)\) isJEE Mains 2019 Hard
- If \(a=\lim _{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}\) and \(b=\lim _{x \rightarrow 0} \) \(\frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}\), then the value of \(a b^3\) isJEE Mains 2024 Hard
- Let \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}-2 \hat{k}\) and \(\overrightarrow{ c }=-\hat{ i }+4 \hat{ j }+3 \hat{ k }\). If \(\overrightarrow{ d }\) is a vector perpendicular to both \(\vec{b}\) and \(\overrightarrow{ c }\) and \(\overrightarrow{ a } \cdot \overrightarrow{ d }=18\), Then \(|\overrightarrow{ a } \times \overrightarrow{ d }|^2\) is equal to \(..........\).JEE Mains 2023 Hard
- Let \(\mathrm{C}\) be the circle of minimum area touching the parabola \(y=6-x^2\) and the lines \(y=\sqrt{3}|x|\). Then, which one of the following points lies on the circle \(C\)?JEE Mains 2024 Hard
- Two integers \(\mathrm{x}\) and \(\mathrm{y}\) are chosen with replacement from the set \(\{0,1,2,3, \ldots ., 10\}\). Then the probability that \(|x-y|>5\) is :JEE Mains 2024 Hard
- Let \(S\) be the set of all values of \(a_1\) for which the mean deviation about the mean of \(100\) consecutive positive integers \(a _1, a _2, a _3, \ldots ., a _{100}\) is \(25\). Then \(S\) isJEE Mains 2023 Hard