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

If $\sinh ^{-1}(2)+\sinh ^{-1}(3)=\alpha$, then $\sinh \alpha=$

A

$2 \sqrt{5}+3 \sqrt{10}$

B

$2 \sqrt{10}+4 \sqrt{5}$

C

$3 \sqrt{10}+4 \sqrt{5}$

D

$2 \sqrt{10}+3 \sqrt{5}$

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

If $x=3-2 \sqrt{3} \mathrm{i}$, then $x^4-12 x^3+54 x^2-108 x-54=$

A

0

B

6

C

-6

D

9

3
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$z_1, z_2, z_3$ represent the vertices $A, B, C$ of a $\triangle A B C$ respectively in the argand plane. If $\left|z_1-z_2\right|=\sqrt{25-12 \sqrt{3}},\left|\frac{z_1-z_3}{z_2-z_3}\right|=\frac{3}{4}$ and $\angle A C B=30^{\circ}$, then the area (in sq units) of that triangle is

A

$\frac{3}{2}$

B

3

C

5

D

$\frac{5}{2}$

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

The product of the four values of the complex number $(1+i)^{3 / 4}$ is

A

$2(1+i)$

B

$2(1-i)$

C

$2^3(1+i)$

D

$2^3(1-i)$

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