1
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\tan ^{-1} x=\cot h^{-1} y=\log \sqrt{5}$, then $\tan ^{-1}(x y)=$

A

$\frac{\pi}{4}$

B

$\frac{\pi}{3}$

C

$\frac{\pi}{6}$

D

$\frac{3 \pi}{4}$

2
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=2+\left|\sin ^{-1} x\right|$ and $A=\left\{x \in R / f^1(x)\right.$ exists $\}$, then $A=$

A

$\{0\}$

B

$[-1,1]$

C

$(-\infty,-1) \cup(1, \infty)$

D

$(-1,0) \cup(0,1)$

3
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The equation $\cos ^{-1}(1-x)-2 \cos ^{-1} x=\frac{\pi}{2}$ has

A

no solution

B

only one solution

C

two solutions

D

more than two solutions

4
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \tan \left(2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\right)= $$

A

$\frac{1}{\sqrt{3}}$

B

$\sqrt{3}$

C

1

D

$3 / 7$

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