1
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $A=\left[\begin{array}{ccc}a & b & c \\ d & e & f \\ l & m & n\end{array}\right]$ is a matrix such that $|A|>0$ and $\operatorname{adj}(A)=\left[\begin{array}{ccc}0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4\end{array}\right]$, then $\frac{c d}{f b}+\frac{\ln }{e m}=$

A

$2 a$

B

$a+m$

C

$a+b$

D

$a$

2
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

In solving a system of linear equations $A X=B$ by Cramer's rule, in the usual notation, if $\Delta_1=\left|\begin{array}{ccc}-11 & 1 & -7 \\ -4 & 1 & -2 \\ 5 & 1 & 1\end{array}\right|$ and $\Delta_3=\left|\begin{array}{ccc}4 & 1 & -11 \\ 1 & 1 & -4 \\ 4 & 1 & 5\end{array}\right|$, then $X=$

A

$\left[\begin{array}{c}-1 \\ 1 \\ 2\end{array}\right]$

B

$\left[\begin{array}{c}2 \\ 1 \\ -1\end{array}\right]$

C

$\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]$

D

$\left[\begin{array}{c}1 \\ 2 \\ -1\end{array}\right]$

3
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $a=\operatorname{Im}\left(\frac{1+z^2}{2 i z}\right)$ and $z$ is any non-zero complex number such that $|z|=1$, then $a=$

A

$\operatorname{Re}(z)$

B

$\operatorname{Re}(z) \operatorname{Im}(z)$

C

$-\operatorname{Re}(z)$

D

$\operatorname{Re}(z)+\operatorname{Im}(z)$

4
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $(3+4 i)^{2025}=5^{2023}(x+i y)$, then $\sqrt{x^2+y^2}=$

A

5

B

25

C

125

D

625