JEE Mains · Maths · STD 12 - 1. relation and function
The number of relations, on the set \(\{1,2,3\}\) containing \((1,2)\) and \((2,3)\), which are reflexive and transitive but not symmetric, is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(A =\{1,2,3\}\) For Reflexive \((1,1)(2,2),(3,3) \in R\) For transitive : \((1,2)\) and \((2,3) \in R \Rightarrow(1,3) \in R\) Not symmetric : \((2,1)\) and \((3,2) \notin R\) \(R _1=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) \(R _2=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(2,1)\}\)…
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
- The mean of a data set consisting of \(20\) observations is \(40\). If one observation \(53\) was wrongly recorded as \(33\), then the correct mean will beJEE Mains 2013 Hard
- Let \(A (2, 3, 5), B (- 1, 3, 2)\) and \(C (\lambda, 5, \mu)\) be the vertices of a \(\Delta ABC\). If the median through \(A\) is equally inclined to the coordinate axes, thenJEE Mains 2014 Hard
- If the curve, \(y = y ( x )\) represented by the solution of the differential equation \(\left(2 x y^{2}-y\right) d x+x d y=0,\) passes through the intersection of the lines, \(2 x -3 y =1\) and \(3 x+2 y=8,\) then \(|y(1)|\) is equal to ...... .JEE Mains 2021 Hard
- Let \(y = y\left( x \right)\) be the solutions of the differential equation, \(\left( {{x^2} + 1} \right)^2\,\frac{{dy}}{{dx}} + 2x\left( {{x^2} + 1} \right)\,y = 1\) such that \(y\left( 0 \right) = 0\). If \(\sqrt a y\left( 1 \right) = \frac{\pi }{{32}}\), then the value of \(‘a’\) isJEE Mains 2019 Hard
- Let the mean and variance of \(8\) numbers \(x , y , 10\), \(12,6,12,4,8\), be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3 x-2 y\) is equal to \(...........\).JEE Mains 2023 Hard
- If \(y = f(x)\) is the solution of the differential equation \(\frac{{dy}}{{dx}} = \left( {\tan \,x - y} \right){\sec ^2}\,x,\,x \in \left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)\), such that \(y(0) = 0\), then \(y\left( { - \frac{\pi }{4}} \right)\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(f\) be any function defined on \(R\) and let it satisfy the condition \(|f( x )-f( y )| \leq\left|( x - y )^{2}\right|, \forall( x , y ) \in R\) If \(f(0)=1,\) thenJEE Mains 2021 Hard
- Let \(\vec{a}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{ c }=2 \hat{ i }-3 \hat{ j }+3 \hat{k}\). If \(\vec{b}\) is \(a\) vector such that \(\vec{a}=\vec{b} \times \vec{c}\) and \(|\vec{b}|^2=50\), then \(|72-| \vec{b}+\left.\vec{c}\right|^2 \mid\) is equal to \(..........\).JEE Mains 2023 Hard
- Let the point, on the line passing through the points \(P(1,-2,3)\) and \(Q(5,-4,7)\), farther from the origin and at a distance of \(9\) units from the point \(\mathrm{P}\), be \((\alpha, \beta, \gamma)\). Then \(\alpha^2+\beta^2+\gamma^2\) is equal to :JEE Mains 2024 Medium
- If \(A\) and \(B\) are any two events such that \(P\left( A \right)\, = \frac{2}{5}\) and \(P\left( {A \cap \,B} \right)\, = \frac{3}{{20}},\) then the conditional probability, \(P\left( {A\,|\,A'\, \cup \,B')} \right),\) where \(A'\) denotes the complement of \(A,\) is equal toJEE Mains 2016 Hard
- If \(A\) and \(B\) are two non-zero \(n \times n\) matrics such that \(A ^2+ B = A ^2 B\), thenJEE Mains 2023 Hard
- The equation of a plane containing the line of intersection of the planes \(2x - y - 4 = 0\) and \(y + 2z - 4 = 0\) and passing through the point \((1, 1, 0)\) isJEE Mains 2019 Medium