1
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

$$\text { If } f(x)=\left|\begin{array}{ccc} x^3 & 2 x^2+1 & 1+3 x \\ 3 x^2+2 & 2 x & x^3+6 \\ x^3-x & 4 & x^2-2 \end{array}\right| \text { for all } x \in \mathbb{R} \text {, then } 2 f(0)+f^{\prime}(0) \text { is equal to }$$

A
24
B
18
C
42
D
48
2
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

Let $$f(x)=(x+3)^2(x-2)^3, x \in[-4,4]$$. If $$M$$ and $$m$$ are the maximum and minimum values of $$f$$, respectively in $$[-4,4]$$, then the value of $$M-m$$ is

A
108
B
392
C
608
D
600
3
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

The maximum area of a triangle whose one vertex is at $$(0,0)$$ and the other two vertices lie on the curve $$y=-2 x^2+54$$ at points $$(x, y)$$ and $$(-x, y)$$, where $$y>0$$, is :

A
108
B
122
C
88
D
92
4
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

The function $$f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}$$

A
decreases in $$(-\infty,-2) \cup(-2,8) \cup(8, \infty)$$
B
increases in $$(-\infty,-2) \cup(-2,8) \cup(8, \infty)$$
C
decreases in $$(-2,8)$$ and increases in $$(-\infty,-2) \cup(8, \infty)$$
D
decreases in $$(-\infty,-2)$$ and increases in $$(8, \infty)$$
EXAM MAP
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