YESPYQ Start Practice
JEEMaths

Let \(N\) be the set of natural numbers and a relation R on N be defined by \(R=\left\{(x,y)\in N\times N:{x}^{3}-3{x}^{…

Q1
PYQ

Let \(N\) be the set of natural numbers and a relation R on N be defined by \(R=\left\{(x,y)\in N\times N:{x}^{3}-3{x}^{2}y-x{y}^{2}+3{y}^{3}=0\right\}\). Then the relation R is :

[JEE Main 2021, 27 Jul (Shift 2)]

a

symmetric but neither reflexive nor transitive

b

reflexive but neither symmetric nor transitive

c

reflexive and symmetric, but not transitive

d

an equivalence relation

🔒
Answer & explanation — PYQ Pass

Options are free to see. Unlock the correct answer and full explanation with Pass.

Unlock · ₹149
← Previous questionNext question →

Practice more JEE Maths PYQs

See every question on Relations and Functions, or browse the full JEE question bank.

See all questions on Relations and Functions →

More JEE Maths PYQs

MathsLet \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). Then the number of many-one functions \(f: A…MathsLet \(f:[0,3] \rightarrow\) A be defined by \(f(x)=2 x^3-15 x^2+36 x+7\) and \(g:[0, \inft…MathsLet \(A=\{-3,-2,-1,0,1,2,3\}\). Let \(R\) be a relation on \(A\) defined by \(x R y\) if a…MathsLet \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). If \(f: A \rightarrow B\), then number of ma…Maths\(\text{ The function }f\left(x\right)=\frac{{x}^{2}+2x-15}{{x}^{2}-4x+9},x\in R\text{ is …MathsDefine a relation \(R\) on the interval \(\left[0, \frac{\pi}{2}\right)\) by \(x R y\) if …