1
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
2
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 $[0,2]$.
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $f(x)$ be continuous on $[0,5]$ and differentiable in $(0,5)$. If $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq \frac{1}{5}$ for all $x$ in $(0,5)$, then $\forall x$ in $[0,5]$

A
$|f(x)| \leq 1$
B
$|f(x)| \leq \frac{1}{5}$
C
$f(x)=\frac{x}{5}$
D
$|f(x)| \geq 1$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

$\lim\limits_{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right)}{\sin ^2 x}$ equals

A
0
B
$\tan 10-10$
C
$\tan 9-9$
D
1
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