1
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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}
2
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
4
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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?

JEE Main 2021 (Online) 17th March Morning Shift Mathematics - Sets and Relations Question 62 English
A
Q and R
B
None of these
C
P and R
D
P and Q
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