Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}x - 1,\,\,\,x < 0\\\,\,\,\,\,\,\frac{1}{4},\,\,x = 0\\\,\,\,\,\,\,\,{x^2},\,\,x > 0\end{array} \right.$, then
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) = 1$
  • B
    $\mathop {\lim }\limits_{x \to 0 - } f(x) = 1$
  • ✓
    $f(x)$ is discontinuous at $x = 0$
  • D
    None of these
✓

Answer

Correct option: C.
$f(x)$ is discontinuous at $x = 0$
c
(c) Clearly from curve drawn of the given function $f(x)$ is discontinuous at $x = 0.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The objective function $Z = 4x + 3y$ can be maximised subjected to the constraints $ 3\text{x}+4\text{y}\leq24,$ $8\text{x}+6\text{y}\leq48,$ $\text{x}\leq5,\text{y}\leq6;\text{x},\text{y}\leq0.$
→
The equation of the curve passing through the origin and satisfying the equation $(1 + {x^2})\frac{{dy}}{{dx}} + 2xy = 4{x^2}$ is
→
Which of the following is a homogeneous differential equation?
→
If two events $A$ and $B$ are independent, then which of the following is true about events $A$ and $B$ ?
→
In a box containing $100$ bulbs, $10$ are defective. What is the probability that out of a sample of $5$ bulbs, none is defective?
→
The differential equation found by the elimination of the arbitrary constant $K$ from the equation $y = (x + K){e^{ - x}}$ is
→
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}}{1+\text{x}^2}$ is:
→
If the function $f(x) = \,\left\{ {\begin{array}{*{20}{c}}{5x - 4}&,&{{\rm{if}}}&{0 < x \le 1}\\{4{x^2} + 3bx}&,&{{\rm{if}}}&{1 < x < 2}\end{array}} \right.$ is continuous at every point of its domain, then the value of $b$ is
→
Which of the following function $(s)$ is/are periodic ?
→
The matrix $\left[ {\begin{array}{*{20}{c}}0&5&{ - 7}\\{ - 5}&0&{11}\\7&{ - 11}&0\end{array}} \right]$is known as
→