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

If the system of equations $2 x+p y+6 z=8$, $x+2 y+q z=5$ and $x+y+3 z=4$ has infinitely many solutions, then $p=$

A

-1

B

2

C

3

D

-3

2
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x^a y^b=e^m, x^c y^d=e^n, \Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|$, $\Delta_2=\left|\begin{array}{cc}a & m \\ c & n\end{array}\right|, \Delta_3=\left|\begin{array}{cc}a & b \\ c & d\end{array}\right|$, then the values of $x$ and $y$ are respectively ( $e$ is the base of natural logarithm)

A

$\frac{\Delta_1}{\Delta_3}$ and $\frac{\Delta_2}{\Delta_3}$

B

$\frac{\Delta_2}{\Delta_1}$ and $\frac{\Delta_3}{\Delta_1}$

C

$\log \left(\frac{\Delta_1}{\Delta_3}\right)$ and $\log \left(\frac{\Delta_2}{\Delta_3}\right)$

D

$e^{\frac{\Delta_1}{\Delta_3}}$ and $e^{\frac{\Delta_2}{\Delta_3}}$

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

If $B$ is the inverse of a third order matrix $A$ and det $B=k$, then $(\operatorname{adj}(\operatorname{adj} \mathrm{A}))^{-1}=$

A

kB

B

$\frac{1}{k} B$

C

$\mathrm{k} B^{-1}$

D

$B+k l$

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

If $A=\left[\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right]$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A-x I|=0$, then $\alpha^2+\beta^2+\gamma^2=$

A

50

B

29

C

17

D

27

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