1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then :
A
$a=3, b=5$
B
$a=0, b=5$
C
$a=0, b=3$
D
$a=b=3$
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :
A
8
B
9
C
3
D
6
3
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.
4
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 $[0,2 a]$.
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