1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $f(x)=|1-2 x|$, then

A
$f(x)$ is continuous but not differentiable at $x=\frac{1}{2}$.
B
$f(x)$ is differentiable but not continuous at $x=\frac{1}{2}$.
C
$f(x)$ is both continuous and differentiable at $x=\frac{1}{2}$.
D
$f(x)$ is neither differentiable nor continuous at $x=\frac{1}{2}$.
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$. If the function ' $f$ ' is differentiable at $x=0$, then $f$ is

A
linear
B
quadratic
C
cubic
D
biquadratic
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is

A
Q
B
R
C
N
D
Z
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect?

A
$f$ is not derivable in $(0,2)$.
B
$f$ is continuous in $[0,2]$.  
C
$f(0)=f(2)$.
D
Rolle's theorem is applicable on $[0,2]$.
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