1
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$, then

A
$$x < y < z$$
B
$$y < z < x$$
C
$$z < x < y$$
D
$$z < y < x$$
2
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\frac{d}{d x}\left\{\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\right\}$$ is equal to

A
0
B
$$\frac{1}{2}$$
C
$$\frac{-1}{2}$$
D
$$-1$$
3
AP EAPCET 2021 - 20th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$y=\tan ^{-1}\left\{\frac{a x-b}{b x+a}\right\}$$, then $$y^{\prime}$$ is equal to

A
$$\frac{1}{1+x^2}+\frac{a^2}{a^2+b^2}$$
B
$$\frac{1}{1+x^2}$$
C
$$\frac{1}{1+\left(\frac{a x-b}{b x+a}\right)^2}$$
D
$$\frac{b x+a}{1+(a x-b)^2}$$
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

For how many distinct values of $$x$$, the following $$\sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0$$ holds?

A
8
B
2
C
6
D
4
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