JEE Main 2022 (Online) 28th June Evening Shift | Sets and Relations Question 44 | Mathematics

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JEE Main 2022 (Online) 28th June Evening Shift

MCQ (Single Correct Answer)

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Let R₁ = {(a, b) $$\in$$ N $$\times$$ N : |a $$-$$ b| $$\le$$ 13} and

R₂ = {(a, b) $$\in$$ N $$\times$$ N : |a $$-$$ b| $$\ne$$ 13}. Then on N :

Both R₁ and R₂ are equivalence relations

Neither R₁ nor R₂ is an equivalence relation

R₁ is an equivalence relation but R₂ is not

R₂ is an equivalence relation but R₁ is not

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

Which of the following is not correct for relation R on the set of real numbers ?

(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.

(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.

JEE Main 2021 (Online) 26th August Morning Shift

MCQ (Single Correct Answer)

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Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

{80, 83, 86, 89}

{84, 86, 88, 90}

{79, 81, 83, 85}

{84, 87, 90, 93}

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

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

symmetric but neither reflexive nor transitive

reflexive but neither symmetric nor transitive

reflexive and symmetric, but not transitive

an equivalence relation

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