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

The value of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x| < \frac{1}{2}, x \neq 0$$

A
$$\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x^2$$
B
$$\frac{\pi}{4}+\cos ^{-1} x^2$$
C
$$\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x^2$$
D
$$\frac{\pi}{4}-\cos ^{-1} x^2$$
2
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
$$\frac{3 \pi}{10}$$
3
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
$$\frac{24}{23}$$
4
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
$$\frac{4}{9} \sin ^2 \alpha$$
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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