1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$$ is

A
$$\frac{5 \pi}{6}$$
B
$$\frac{\pi}{2}$$
C
$$\frac{2 \pi}{3}$$
D
$$\frac{3 \pi}{4}$$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$

A
$$\frac{\pi}{8}$$
B
$$-\frac{\pi^2}{8}$$
C
$$\frac{\pi^2}{4}$$
D
$$-\frac{\pi^2}{4}$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$$, then which of the following statement is true?

A
$$a+b-c=a b c$$
B
$$a+b+c=2 a b c$$
C
$$\mathrm{abc}=1$$
D
$$a+b+c=a b c$$
4
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\frac{4}{x^4}\left[1-\cos \frac{x}{2}-\cos \frac{x}{4}+\cos \frac{x}{2} \cdot \cos \frac{x}{4}\right]$$ is continuous at $$x=0$$, then $$\mathrm{f}(0)$$ is

A
$$\frac{1}{32}$$
B
$$\frac{1}{16}$$
C
$$\frac{1}{8}$$
D
$$\frac{1}{64}$$
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