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

The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has

A
two points of local maximum.
B
two points of local minimum.
C
one local maximum and one local minimum.
D
neither maximum nor minimum.
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is

A
increasing on $[0, a]$.
B
decreasing on $[0, a]$.
C
increasing on $[0,2 a]$.
D
decreasing on $[0,2 a]$.
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

A
$f(x)=\sin ^2 x, g(x)=\sqrt{x}$
B
$f(x)=\sin x, g(x)=|x|$
C
$f(x)=x^2, g(x)=\sin \sqrt{x}$
D
$f(x)=|x|, g(x)=\sin x$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The expression $2^{4 n}-15 n-1$, where $n \in \mathbb{N}$ (the set of natural numbers) is divisible by

A
125
B
225
C
325
D
425
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