1
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
2
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
3
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 $$(8, \infty)$$
4
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

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

A
exactly one point of local minima and no point of local maxima
B
exactly one point of local maxima and exactly one point of local minima
C
exactly two points of local maxima and exactly one point of local minima
D
exactly one point of local maxima and no point of local minima
EXAM MAP
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