1
MHT CET 2023 9th May Evening Shift
+2
-0

The range of values of $$x$$ for which $$f(x)=x^3+6 x^2-36 x+7$$ is increasing in

A
$$(-\infty,-6) \cup(2, \infty)$$
B
$$(-6,2)$$
C
$$(-\infty,-2) \cup(6, \infty)$$
D
$$(-6,2]$$
2
MHT CET 2023 9th May Evening Shift
+2
-0

The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $$\mathrm{S}=\left\{x \in \mathbb{R} / x^2+30 \leq 11 x\right\}$$ is

A
122
B
132
C
112
D
222
3
MHT CET 2023 9th May Evening Shift
+2
-0

A water tank has a shape of inverted right circular cone whose semi-vertical angle is $$\tan ^{-1}\left(\frac{1}{2}\right)$$. Water is poured into it at constant rate of 5 cubic meter/minute. The rate in meter/ minute at which level of water is rising, at the instant when depth of water in the tank is $$10 \mathrm{~m}$$ is

A
$$\frac{1}{5 \pi}$$
B
$$\frac{1}{15 \pi}$$
C
$$\frac{2}{\pi}$$
D
$$\frac{1}{10 \pi}$$
4
MHT CET 2023 9th May Evening Shift
+2
-0

Let $$\mathrm{f}(0)=-3$$ and $$\mathrm{f}^{\prime}(x) \leq 5$$ for all real values of $$x$$. The $$\mathrm{f}(2)$$ can have possible maximum value as

A
10
B
5
C
7
D
13
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