1
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
$$12\sqrt6-\frac{31}{2}$$
2
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
3
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
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 Let $$f(x) = \left\{ {\matrix{ {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \cr { - 2x + {{\log }_2}({b^2} - 4),} & {x > 1} \cr } } \right.$$.

Then the set of all values of b, for which f(x) has maximum value at x = 1, is :

A
($$-$$6, $$-$$2)
B
(2, 6)
C
$$[ - 6, - 2) \cup (2,6]$$
D
$$\left[ {-\sqrt 6 , - 2} \right) \cup \left( {2,\sqrt 6 } \right]$$
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