1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$

and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$

have a common extreme point, then $a+2 b+7$ is equal to :
A
6
B
$\frac{3}{2}$
C
3
D
4
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1
Out of Syllabus

The number of points on the curve $$y=54 x^{5}-135 x^{4}-70 x^{3}+180 x^{2}+210 x$$ at which the normal lines are parallel to $$x+90 y+2=0$$ is :

A
2
B
3
C
4
D
0
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

Let the function $$f(x) = 2{x^3} + (2p - 7){x^2} + 3(2p - 9)x - 6$$ have a maxima for some value of $$x < 0$$ and a minima for some value of $$x > 0$$. Then, the set of all values of p is

A
$$\left( { - {9 \over 2},{9 \over 2}} \right)$$
B
$$\left( {{9 \over 2},\infty } \right)$$
C
$$\left( {0,{9 \over 2}} \right)$$
D
$$\left( { - \infty ,{9 \over 2}} \right)$$
4
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

Let $$x=2$$ be a local minima of the function $$f(x)=2x^4-18x^2+8x+12,x\in(-4,4)$$. If M is local maximum value of the function $$f$$ in ($$-4,4)$$, then M =

A
$$18\sqrt6-\frac{33}{2}$$
B
$$18\sqrt6-\frac{31}{2}$$
C
$$12\sqrt6-\frac{33}{2}$$
D
$$12\sqrt6-\frac{31}{2}$$
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