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

Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$, then

A
$f(4)<8$
B
$f(4) \geq 12$
C
$f(4) \geq 8$
D
$f(4)<12$
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then

A
$\alpha=-6, \beta=\frac{1}{2}$
B
$\alpha=-6, \beta=-\frac{1}{2}$
C
$\alpha=2, \beta=-\frac{1}{2}$
D
$\alpha=2, \beta=\frac{1}{2}$
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|$. Suppose $A$ and $B$ are respectively maximum and minimum values of $f(\theta)$.Then $(A,B)$ is equal to

A
$(2,1)$
B
$(2,0)$
C
$(\sqrt{2}, 1)$
D
$\left(2, \frac{1}{\sqrt{2}}\right)$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The maximum number of common normals of $y^2=4 a x$ and $x^2=4 b y$ is equal to

A
3
B
4
C
5
D
6
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