WB JEE 2021 | Sets and Relations Question 22 | Mathematics

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

Let R be the real line. Let the relations S and T or R be defined by

$$S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y$$ is an integer}. Then

both S and T are equivalence relations on R

T is an equivalence on R but S is not

neither S nor T is an equivalence relation on R

S is an equivalence relation on R but T is not

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then

p is equivalence relation

p is reflexive and symmetric but is not transitive

p is reflexive and transitive but is not symmetric

p is reflexive only

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then f is

injective but not surjective

surjective but not injective

neither injective nor surjective

bijective

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

Let p₁ and p₂ be two equivalence relations defined on a non-void set S. Then

both p₁ $$ \cap $$ p₂ and p₁ $$ \cup $$ p₂ are equivalence relations

$${p_1} \cap {p_2}$$ is equivalence relation but $${p_1} \cup {p_2}$$ is not so

$${p_1} \cup {p_2}$$ is equivalence relation but $${p_1} \cap {p_2}$$ is not so

neither $${p_1} \cap {p_2}$$ nor $${p_1} \cup {p_2}$$ is equivalence relation.

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Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Atomic Structure Redox Reaction Gaseous State Chemical Equilibrium Liquid Solution Ionic Equilibrium Thermodynamics Chemical Kinetics Radioactivity and Nuclear Chemistry Electrochemistry Solid State Surface Chemistry

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Periodic Table Chemical Bonding Metallurgy Hydrogen and It's Compounds Some s Block Elements Some P Block Elements d and f Block Elements Coordination Compounds

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IUPAC Nomenclatures General Organic Chemistry Isomerism Hydrocarbons Halogen Derivatives Alcohol and Ether Aldehyde and Ketone Aromatic Chemistry Carbonyl Compounds Carboxylic Acids and Amines Polymers Biomolecules Practical Chemistry Chemistry In Everyday Life

Mathematics

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Logarithms Sequence and Series Quadratic Equations Complex Numbers Permutations and Combinations Mathematical Induction and Binomial Theorem Matrices and Determinants Vector Algebra Three Dimensional Geometry Probability Statistics Sets and Relations

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Properties of Triangle Inverse Trigonometric Functions Trigonometric Functions & Equations

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Straight Lines and Pair of Straight Lines Circle Parabola Ellipse and Hyperbola

Calculus

Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integrals Definite Integration Application of Integration Differential Equations