1
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The number of values of $x$ satisfying the equation, $\tan ^{-1}\left(x+\frac{\sqrt{2}}{x}\right)+\tan ^{-1}\left(x-\frac{\sqrt{2}}{x}\right)=\tan ^{-1}(x)$ is

A

0

B

1

C

2

D

3

2
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=\sec ^{-1} x$, then $\frac{d^2 y}{d x^2}=$

A

$\frac{1-2 x^2}{x|x|\left(x^2-1\right)^{\frac{3}{2}}}$

B

$\frac{1-x^2}{x^2\left(x^2-1\right)^{\frac{3}{2}}}$

C

$\frac{1-x^2}{-x^2\left(x^2-1\right)^{\frac{3}{2}}}$

D

$\frac{1+2 x^2}{x|x|\left(x^2-1\right)^{\frac{3}{2}}}$

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

If $0 \leq x<\frac{3}{4}$, then the number of values of $x$ satisfying the equation $\tan ^{-1}(2 x-1)+\tan ^{-1} 2 x= \tan ^{-1} 4 x-\tan ^{-1}(2 x+1)$ is

A

0

B

1

C

2

D

3

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

If $\sinh ^{-1} x=\cosh ^{-1} y=\log (1+\sqrt{2})$, then $\tan ^{-1}(x+y)$

A

$67 \frac{1}{2}^{\circ}$

B

$75^{\circ}$

C

$22 \frac{1}{2}^{\circ}$

D

$15^{\circ}$

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