1
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
$|f(x)| \geq 1$
2
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
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of points in $[\alpha,\beta]$ at which $f$ is not differentiable is

A
2
B
0
C
1
D
infinite
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $\lim \limits_{n \rightarrow \infty} \frac{\left(a_n\right) n!}{{ }^{3 n} P_n}$ equals

A
0
B
1
C
e
D
e/$\sqrt3$
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