JEE Main 2022 (Online) 29th June Morning Shift | Sets and Relations Question 43 | Mathematics

JEE Main 2022 (Online) 29th June Morning Shift

MCQ (Single Correct Answer)

-1

Let a set A = A₁ $$\cup$$ A₂ $$\cup$$ ..... $$\cup$$ A_k, where A_i $$\cap$$ A_j = $$\phi$$ for i $$\ne$$ j, 1 $$\le$$ j, j $$\le$$ k. Define the relation R from A to A by R = {(x, y) : y $$\in$$ A_i if and only if x $$\in$$ A_i, 1 $$\le$$ i $$\le$$ k}. Then, R is :

reflexive, symmetric but not transitive.

reflexive, transitive but not symmetric.

reflexive but not symmetric and transitive.

an equivalence relation.

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)

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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)

-1

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}

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