1
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

  • $A=\left[\begin{array}{ccc}0 & k & k \\ k & -4 & -6 \\ k & -3 & -5\end{array}\right]$ is a singular matrix for
  • A

    $k=2$ only

    B

    $k= \pm 2$ only

    C

    no real value of $k$

    D

    all real values of $k$

    2
    AP EAPCET 2025 - 23rd May Morning Shift
    MCQ (Single Correct Answer)
    +1
    -0

    If $A=\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ and the rank of $A$ is 2 , then the value of $x$ is equal to

    A

    1

    B

    0

    C

    -3

    D

    3

    3
    AP EAPCET 2025 - 23rd May Morning Shift
    MCQ (Single Correct Answer)
    +1
    -0

    $$ \left|\begin{array}{ll} 2 & 1 \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} 1 & \frac{1}{3} \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} \frac{1}{2} & \frac{1}{9} \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} \frac{1}{4} & \frac{1}{27} \\ 3 & 1 \end{array}\right|+\ldots \infty= $$

    A

    0

    B

    $1 / 2$

    C

    $-1 / 2$

    D

    -1

    4
    AP EAPCET 2025 - 23rd May Morning Shift
    MCQ (Single Correct Answer)
    +1
    -0

    For any two non-zero complex numbers $z_1$ and $z_2$, if $\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2$, then

    A

    $\operatorname{Re}\left(\frac{z_1}{z_2}\right)=0$

    B

    $\operatorname{lm}\left(\frac{z_1}{z_2}\right)=0$

    C

    $\operatorname{Re}\left(z_1 z_2\right)=0$

    D

    $\operatorname{lm}\left(z_1 z_2\right)=0$