Points of discontinuity of the greatest integer function f(x) = [x], where [x] denotes integer less than or equal to x, are Option 1: all natural numbers Option 2: all rational numbers Option 3: all integers Option 4: all real numbers

The answer is 'all integers'. View full solution:

CUET Mathematics - Points of discontinuity of the greatest integer function f(x) = [x], where [x] denotes integer less than or equal to x, are | PYQs + Solutions

CUET Mathematics 2023 23 May Shift 3

Calculus

Easy

all natural numbers

all rational numbers

all integers

all real numbers

✅ Correct Option: 3

Related questions:

14 May Shift 1

Match List-I with List-II

$\begin{array}{|l|l|} \hline \rule{0pt}{2.8ex}\text{List-I} & \text{List-II} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(A) } f(x) = |x| & \text{(I) Not differentiable at } x=-2 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(B) } f(x) = |x+2| & \text{(II) Not differentiable at } x=0 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(C) } f(x) = |x^2-4| & \text{(III) Not differentiable at } x=2 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(D) } f(x) = |x-2| & \text{(IV) Not differentiable at } x=2,-2 \text{ only} \\[1.2ex] \hline \end{array}$

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16 July Shift 2

Match List I with List II

List I	List II
A. If $f(x) = 2x$ and $g(x) = \frac{x^2}{2} + 1$ , then $\frac{g(x)}{f(x)}$ is	I. discontinuous at exactly three points.
B. The function $f(x) = \frac{4-x^2}{4x-x^3}$ is	II. continuous everywhere
C. The function $f(x) =	x
D. The function $f(x) =	\sin x

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25 May Shift 1

The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$ , is discontinuous at

CUET Mathematics 2023 23 May Shift 3 PYQs

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