Class 12

03. Sets and Relations question bank (Maths)

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Q1.

Which of the following statement(s) is/are true for \( f(x) = [x] \) (where [.] is greatest integer function)?

(A)

\( f(1^+) = f(2^+) = f(3^+) \)

(B)

\( f(4^+) < f(3^+) \)

(C)

\( f(2^-) = f(3^-) \)

(D)

\( f(0^-) = f(5^-) \)

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Q2.

Range of the function \( f \) defined by \( f(x) = \left[ \frac{1}{\{x\}} \right] \),
where [.] and \(\{.\}\) denote the greatest integer and fractional part function respectively, is

(A)

set of integers

(B)

set of all natural numbers

(C)

\{2, 3, 4, \ldots\}

(D)

\{1\}

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