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

The maximum value of xy when x + 2y = 8 is

A
20
B
16
C
24
D
8
4
MHT CET 2023 9th May Morning Shift
+2
-0

An object is moving in the clockwise direction around the unit circle $$x^2+y^2=1$$. As it passes through the point $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$, its $$y$$-co-ordinate is decreasing at the rate of 3 units per sec. The rate at which the $$x$$-co-ordinate changes at this point is

A
2 units/sec
B
$$3 \sqrt{3}$$ units/sec
C
$$\sqrt{3}$$ units /sec
D
$$2 \sqrt{3}$$ units /sec
EXAM MAP
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