enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}\) be a relation on the set \(A= \{3, 5, 9, 12\}.\) Then, \(R\) is
- A reflexive, symmetric but not transitive.
- B symmetric, transitive but not reflexive.
- C an equivalence relation.
- D reflexive, transitive but not symmetric.
Answer & Solution
Correct Answer
(D) reflexive, transitive but not symmetric.
Step-by-step Solution
Detailed explanation
Let \(R = \left\{ {\left( {3,3} \right),\left( {5,5} \right),\left( {9,9} \right),\left( {12,12} \right),\left( {5,12} \right),\left( {3,9} \right),\left( {3,12} \right),\left( {3,5} \right)} \right\}\) be arelation on set \(A = \left\{ {3,5,9,12} \right\}\) Clearly, every…
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 the equations of two ellipses be \({E_1}:\,\frac{{{x^2}}}{3} + \frac{{{y^2}}}{2} = 1\) and \({E_2}:\,\frac{{{x^2}}}{16} + \frac{{{y^2}}}{b^2} = 1,\) If the product of their eccentricities is \(\frac {1}{2},\) then the length of the minor axis of ellipse \(E_2\) isJEE Mains 2013 Hard
- Let the arc \(A C\) of a circle subtend a right angle at the centre \(O\). If the point \(B\) on the arc \(A C\), divides the arc \(A C\) such that \(\frac{\text { length of } \operatorname{arc} A B}{\text { length of } \operatorname{arc} B C}=\frac{1}{5}\), and \(\overrightarrow{O C}=\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}\), then \(\alpha+\sqrt{2}(\sqrt{3}-1) \beta\) is equal toJEE Mains 2025 Easy
- Let \(y = y(x)\) be the solution of the differential equation \(\frac{{dy}}{{dx}} + y\,\tan \,x = 2x\, + \,{x^2}\,\tan \,x\,,\,x\, \in \,\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right),\) such that \(y(0) = 1.\) ThenJEE Mains 2019 Hard
- Let a variable line passing through the centre of the circle \(x^2+y^2-16 x-4 y=0\), meet the positive co-ordinate axes at the point \(\mathrm{A}\) and \(\mathrm{B}\). Then the minimum value of \(\mathrm{OA}+\mathrm{OB}\), where \(\mathrm{O}\) is the origin, is equal toJEE Mains 2024 Hard
- A bag contains \(4\) red and \(6\) black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are re turned to the bag. Ifnow a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :JEE Mains 2018 Hard
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\) where \(x \in R\;\) and \(k \ge 1\). Then \({f_4}\left( x \right) - {f_6}\left( x \right) \) is equalsJEE Mains 2014 Hard
More PYQs from JEE Mains
- The equation of the plane containing the line \(2x- 5y+ z = 3; x +y+ 4z = 5,\) and parallel to the plane, \(x + 3y+ 6z = 1,\) is:JEE Mains 2015 Medium
- A hyperbola passes through the foci of the ellipse \(\frac{ x ^{2}}{25}+\frac{ y ^{2}}{16}=1\) and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities in one, then the equation of the hyperbola is ...... .JEE Mains 2021 Medium
- Consider the parabola with vertex \(\left(\frac{1}{2}, \frac{3}{4}\right)\) and the directrix \(\mathrm{y}=\frac{1}{2}\). Let \(\mathrm{P}\) be the point where the parabola meets the line \(\mathrm{x}=-\frac{1}{2}\). If the normal to the parabola at \(\mathrm{P}\) intersects the parabola again at the point \(\mathrm{Q}\), then \((\mathrm{PQ})^{2}\) is equal to :JEE Mains 2021 Hard
- The point of intersection \(C\) of the plane \(8 x+y+2 z=0\) and the line joining the points \(A (-3,-6,1)\) and \(B (2,4,-3)\) divides the line segment \(AB\) internally in the ratio \(k : 1\). If \(a , b , c\) \((| a |,| b |,| c |\) are coprime) are the direction ratios of the perpendicular from the point \(C\) on the line \(\frac{1- x }{1}=\frac{ y +4}{2}=\frac{z+2}{3}\), then \(|a + b + c|\) is equal to \(.............\).JEE Mains 2023 Hard
- The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1, x = 0\) and \(x = 3\), isJEE Mains 2019 Hard
- Let \(f\) be a composite function of \(x\) defined by \(f\left( u \right) = \frac{1}{{{u^2} + u - 2}}\,,\,u\left( x \right) = \frac{1}{{x - 1}}\) . Then the number of points \(x\) where \(f\) is discontinuous isJEE Mains 2013 Hard