1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$$, then the value of $$\cos ^{-1} x+\sin ^{-1} y$$ is

A
$$\frac{\pi}{10}$$
B
$$\frac{7 \pi}{10}$$
C
$$\frac{9 \pi}{10}$$
D
$$\frac{3 \pi}{10}$$
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is

A
30
B
$$\frac{53}{3}$$
C
16
D
18
3
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of $$\mathrm{A}$$ are $$4: 6$$, the odds against $$B$$ are $$7: 3$$. Thus, odds against $$\mathrm{C}$$ are

A
$$7: 3$$
B
$$4: 6$$
C
$$6: 4$$
D
$$3: 7$$
4
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+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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