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

The value of $$\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)$$ is

A
$$\frac{23}{25}$$
B
$$\frac{25}{23}$$
C
$$\frac{23}{24}$$
D
$$\frac{24}{23}$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y$$ $$9 x^2-6 x y \cos \alpha+y^2$$ is equal to

A
$$\sin ^2 \alpha$$
B
$$3 \sin ^2 \alpha$$
C
$$9 \sin ^2 \alpha$$
D
$$\frac{4}{9} \sin ^2 \alpha$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x}=$$

A
$$\frac{1}{1+x^2}-\frac{1}{1+(x+2)^2}$$
B
$$\frac{-1}{1+x^2}+\frac{1}{1+(x+2)^2}$$
C
$$\frac{1}{1+x^2}+\frac{1}{1+(x+2)^2}$$
D
$$\frac{-1}{1+x^2}-\frac{1}{1+(x+2)^2}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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