WB JEE 2022 | Sets and Relations Question 18 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defined. Let g . f be injective mapping. Then

f, g both are injective.

neither f nor g is injective.

f is obviously injective.

g is obviously injective.

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

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