List of top Questions asked in AP EAMCET- 2022

If
\[ iz^3+z^2-z+i=0, \] then \(|z|=\)

If
\[ \frac{x-1}{3+i}+\frac{y-1}{3-i}=i, \] then the true statement among the following is

The number of integer solutions of the equation
\[ |1-i|^x=2^x \] is

If \(f(x)=ax^2+bx+c\) for some \(a,b,c\in \mathbb{R}\) with \(a+b+c=3\) and
\[ f(x+y)=f(x)+f(y)+xy \quad \forall x,y\in \mathbb{R}, \] then
\[ \sum_{n=1}^{10} f(n)= \]

Let
\[ A= \begin{bmatrix} 5 & \sin^2\theta & \cos^2\theta \\ -\sin^2\theta & -5 & 1 \\ \cos^2\theta & 1 & 5 \end{bmatrix} \] Then, the maximum value of \(\det(A)\) is

If \(f(x)=\sqrt{2-x^2}\) and \(g(x)=\log(1-x)\) are two real valued functions, then the domain of the function \((f+g)(x)\) is

For \(i=1,2,3\) and \(j=1,2,3\), if
\[ a_i^2+b_i^2+c_i^2=1 \] and
\[ a_ia_j+b_ib_j+c_ic_j=0 \quad \forall \; i\neq j \] and
\[ A= \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \] then \(\det(AA^T)=\)

If
\[ A=\frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}, \] then

If
\[ A= \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix} \] and
\[ \det(A^{10})=1024, \] then \(\alpha=\)

The range of the real valued function \(f(x)=\sqrt{\dfrac{x^2+2x+8}{x^2+2x+4}}\) is