1
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
$$\left( { - \infty ,{9 \over 2}} \right)$$
2
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
$$12\sqrt6-\frac{31}{2}$$
3
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 Let $$f(x)=3^{\left(x^{2}-2\right)^{3}+4}, x \in \mathrm{R}$$. Then which of the following statements are true?

$$\mathrm{P}: x=0$$ is a point of local minima of $$f$$

$$\mathrm{Q}: x=\sqrt{2}$$ is a point of inflection of $$f$$

$$R: f^{\prime}$$ is increasing for $$x>\sqrt{2}$$

A
Only P and Q
B
Only P and R
C
Only Q and R
D
All P, Q and R
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1 If the minimum value of $$f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$$, is 14 , then the value of $$\alpha$$ is equal to :

A
32
B
64
C
128
D
256
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