1
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
$$\sqrt{3}$$
2
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
3
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
4
MHT CET 2023 9th May Morning Shift
+2
-0

A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is $$3 \mathrm{~mm}$$ and 1 hour later it reduces to $$2 \mathrm{~mm}$$, then the expression for the radius $$R$$ of the raindrop at any time $$t$$ is

A
$$6 \mathrm{R}=\mathrm{t}+2$$
B
$$\mathrm{R}(\mathrm{t}+2)=6$$
C
$$\mathrm{R}=6(\mathrm{t}+2)$$
D
$$6 \mathrm{R}=\mathrm{t}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
EXAM MAP
Joint Entrance Examination