1
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
reflexive, symmetric but not transitive.
B
reflexive, transitive but not symmetric.
C
reflexive but not symmetric and transitive.
D
an equivalence relation.
2
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
Both R1 and R2 are equivalence relations
B
Neither R1 nor R2 is an equivalence relation
C
R1 is an equivalence relation but R2 is not
D
R2 is an equivalence relation but R1 is not
3
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Which of the following is not correct for relation R on the set of real numbers ?
A
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.
B
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.
C
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.
D
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.
4
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-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 :
A
{80, 83, 86, 89}
B
{84, 86, 88, 90}
C
{79, 81, 83, 85}
D
{84, 87, 90, 93}
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