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Functions question

2023 · 6 Apr · Shift 2 · Q36

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PYQ Library
JEE Main
Mathematics
Functions
2023 · 6 Apr · Shift 2 · Q36

Functions question

2023 · 6 Apr · Shift 2 · Q36

JEE MainMathematicsFunctionsMCQ+4 / −1

Let the sets A and B denote the domain and range respectively of the function

f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}

, where

\lceil x\rceil

denotes the smallest integer greater than or equal to

x

. Then among the statements (S1) :

A \cap B=(1, \infty)-\mathbb{N}

and (S2) :

A \cup B=(1, \infty)

A
only $(\mathrm{S} 2)$ is true
B
only (S1) is true
C
neither (S1) nor (S2) is true
D
both (S1) and (S2) are true

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