WB JEE 2022 | Sets and Relations Question 19 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is correct?

f is one-one but not onto

f is onto but not one-one

f is neither one-one nor onto

f is both one-one and onto

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote the complement of set C in S. Then

A $$\cap$$ B = $$\phi$$

A $$\cap$$ B $$\ne$$ $$\phi$$

A $$\cap$$ C = A

A $$\cup$$ C = A

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

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