1
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
$$\frac{1}{10 \pi}$$
2
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
3
MHT CET 2023 9th May Morning Shift
+2
-0

The value of $$c$$ of Lagrange's mean value theorem for $$f(x)=\sqrt{25-x^2}$$ on $$[1,5]$$ is

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

The value of $$\alpha$$, so that the volume of the parallelopiped formed by $$\hat{i}+\alpha \hat{j}+\hat{k}, \hat{j}+\alpha \hat{k}$$ and $$\alpha \hat{i}+\hat{k}$$ becomes maximum, is

A
$$\frac{-1}{\sqrt{3}}$$
B
$$\frac{1}{\sqrt{3}}$$
C
$$-\sqrt{3}$$
D
$$\sqrt{3}$$
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