1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+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
$$\frac{4}{9} \sin ^2 \alpha$$
2
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+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
$$\frac{-1}{1+x^2}-\frac{1}{1+(x+2)^2}$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$

A
$$\frac{56}{65}$$
B
$$\frac{61}{65}$$
C
$$\frac{63}{65}$$
D
$$\frac{62}{65}$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$$ are

A
$$\pm \frac{3}{\sqrt{2}}$$
B
$$\pm \frac{1}{2}$$
C
$$\pm \frac{1}{\sqrt{2}}$$
D
$$\pm \frac{\sqrt{3}}{2}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
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