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 2023 (Online) 25th January Morning Shift
+4
-1

Let $$f:(0,1)\to\mathbb{R}$$ be a function defined $$f(x) = {1 \over {1 - {e^{ - x}}}}$$, and $$g(x) = \left( {f( - x) - f(x)} \right)$$. Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0, 1)

Then,

A
Both (I) and (II) are true
B
Neither (I) nor (II) is true
C
Only (II) is true
D
Only (I) is true
4
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
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