1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right|>0$, then $a b c>$
A
1
B
-8
C
8
D
3
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    If the system of equations $a_1 x+b_1 y+c_1 z=0, a_2 x+b_2 y+c_2 z=0$ and $a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ is

A
2
B
1
C
3
D
0
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\omega$ is a complex cube root of unity and if $z$ is a complex number satisfying $|z-1| \leq 2$ and $\left|\omega^2 z-1-\omega\right|=a$, then the set of possible values of $a$ is
A
$0 \leq a \leq 2$
B
$\frac{1}{2} \leq a \leq \frac{\sqrt{3}}{2}$
C
$|\omega| \leq a \leq \frac{\sqrt{3}}{2}+2$
D
$0 \leq a \leq 4$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the roots of the equation $z^3+i z^2+2 i=0$ are the vertices of a $\triangle A B C$, then that $\triangle A B C$ is
A
a right angled triangle
B
an equilateral triangle
C
an isosceles triangle
D
a right angled isosceles triangle
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