1
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
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Define a relation R over a class of n $$\times$$ n real matrices A and B as

"ARB iff there exists a non-singular matrix P such that PAP$$-$$1 = B".

Then which of the following is true?
A
R is reflexive, transitive but not symmetric
B
R is symmetric, transitive but not reflexive.
C
R is reflexive, symmetric but not transitive
D
R is an equivalence relation
3
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

A
Q and R
B
None of these
C
P and R
D
P and Q
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Let A = {2, 3, 4, 5, ....., 30} and '$$\simeq$$' be an equivalence relation on A $$\times$$ A, defined by (a, b) $$\simeq$$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :
A
5
B
6
C
8
D
7
EXAM MAP
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