JEE Main 2021 (Online) 31st August Morning Shift | Sets and Relations Question 84 | Mathematics

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}

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-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 :

symmetric but neither reflexive nor transitive

reflexive but neither symmetric nor transitive

reflexive and symmetric, but not transitive

an equivalence relation

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

-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?

R is reflexive, transitive but not symmetric

R is symmetric, transitive but not reflexive.

R is reflexive, symmetric but not transitive

R is an equivalence relation

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