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

The number of real solution of $\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}$ is

A

2

B

1

C

0

D

infinitely many

2
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Consider the following

Assertion

$$ \begin{aligned} & \text { (A) } \begin{array}{r} \sqrt{x-3}\left(\sin ^{-1}(\log x)+\cos ^{-1}\right. \\ (\log x) d x=\frac{\pi}{3}(x-3)^{3 / 2}+c \end{array} \end{aligned} $$

Reason $(\mathrm{R}) \sin ^{-1}(f(x))+\cos ^{-1}(f(x))=\frac{\pi}{2},|f(x)|<1$

The correct answer is

A

Both $(A)$ and $(B)$ are true and $(R)$ is the correct explanation of $(A)$.

B

Both (A) and (R) are true and (R) is not the correct explanation of (A).

C

(A) is true, but (R) is false.

D

(A) is false, but (R) is true.

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \sin ^{-1}(-\cos 2)+\cos ^{-1}(\sin 3)+\tan ^{-1}(\cot 5)= $$

A

7

B

5

C

$\frac{\pi}{2}$

D

$\pi$

4
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The domain of the derivative of the function $f(x)=\cos ^{-1}(2 x-5)-\sin ^{-1}(x-2)$ is

A

$[2,3]$

B

$(-\infty, 2] \cup[3, \infty)$

C

$(-\infty, 2) \cup(3, \infty)$

D

$(2,3)$

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