1
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

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
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
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.
3
JEE Main 2021 (Online) 26th August Morning Shift
+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}
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-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 :
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
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