JEE Mains · Maths · STD 12 - 1. relation and function
The relation \(R=\{(x, y): x, y \in \mathbb{Z}\) and \(x+y\) is even \(\}\) is:
- A reflexive and symmetric but not transitive
- B an equivalence relation
- C symmetric and transitive but not reflexive
- D reflexive and transitive but not symmetric
Answer & Solution
Correct Answer
(B) an equivalence relation
Step-by-step Solution
Detailed explanation
For reflexive \((x, x) \in \mathbb{R}, x \in \mathbb{Z}\) \(\Rightarrow x+x=2 x \rightarrow \text { even }\) For symmetric of \((x, y) \in \mathbb{R}\) then \((y, x) \in \mathbb{R}\) when \(x, y \in \mathbb{Z}\) \(x+y \rightarrow\) even…
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 value of \(\lim\limits _{n \rightarrow \infty} 6 \tan \left\{\sum\limits_{r=1}^{n} \tan ^{-1}\left(\frac{1}{r^{2}+3 r+3}\right)\right\}\) is equal toJEE Mains 2022 Hard
- A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point \(A\) on the path, he observes that the angle of elevation of the top of the pillar is \(30^o .\) After walking for \(10\) minutes from \(A\) in the same direction, at a point \(B,\) he observes that the angle of elevation of the top of the pillar is \(60^o .\) Then the time taken (in minutes) by him, from \(B\) to reach the pillar, is:JEE Mains 2016 Hard
- Let the range of the function \(f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \operatorname{IR} \text { be }[a, b] .\) If \(\alpha\) and \(\beta\) are respectively the \(A.M.\) and the \(G.M.\) of a and \(b\), then \(\frac{\alpha}{\beta}\) is equal to :JEE Mains 2024 Hard
- The equation \(y = \sin \,x\,\sin \,\left( {x + 2} \right) - {\sin ^2}\,\left( {x + 1} \right)\) represents a straight line lying inJEE Mains 2019 Hard
- Let \(A,B\) be points on the two half-lines \(x-\sqrt{3}|y|=\alpha\), \(\alpha>0\) at a distance of \(\alpha\) from their point of intersection \(P\). The line segment \(AB\) meets the angle bisector of the given half-lines at the point \(Q\). If \(PQ=\dfrac{9}{2}\) and \(R\) is the radius of the circumcircle of \(\triangle PAB\), then \(\dfrac{\alpha^2}{R}\) is equal to ______JEE Mains 2026 Hard
- Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y+\) \(z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin isJEE Mains 2022 Medium
More PYQs from JEE Mains
- For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :JEE Mains 2024 Medium
- The angle between the straight lines, whose direction cosines are given by the equations \(2 l+2 \mathrm{~m}-\mathrm{n}=0\) and \(\mathrm{mn}+\mathrm{n} l+l \mathrm{~m}=0\), is :JEE Mains 2021 Hard
- The lowest integer which is greater than \(\left(1+\frac{1}{10^{100}}\right)^{10^{100}}\) is \(.....\)JEE Mains 2021 Hard
- Let the coefficients of \(x ^{-1}\) and \(x ^{-3}\) in the expansion of \(\left(2 x^{\frac{1}{5}}-\frac{1}{x^{\frac{1}{5}}}\right)^{15}, x>0\), be \(m\) and \(n\) respectively. If \(r\) is a positive integer such \(m n^{2}={ }^{15} C _{ r } .2^{ r }\), then the value of \(r\) is equal toJEE Mains 2022 Medium
- Let \(f: R \rightarrow R\) be defined as \(f(\mathrm{x})= -\frac{4}{3} x^{3}+2 x^{2}+3 x ,\quad x>0\) \(\quad\quad\quad\quad 3 x e^{x}, \quad\quad\quad\quad\quad\quad\mathrm{x} \leq 0\) Then \(\mathrm{f}\) is increasing function in the interval.JEE Mains 2021 Medium
- If the domain of the function \(f(x) = \sqrt{\log_{(0.6)}\left(\left|\dfrac{2x-5}{x^2-4}\right|\right)}\) is \((-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)\), then the value of \(a + b + c + d + e\) is _______.JEE Mains 2026 Hard