Algebra - Mathematics PYQ | AP EAPCET

$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}$ is a point on the line parallel to the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{k}}$. If $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ is a point on the plane parallel to the vectors $2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{k}}$, then the point of intersection of the line and the plane is

If the values of $k$ for which the euqation $x^2+2(k+2) x+6 k+7=0$ has equal roots are $k_1$ and $k_2$, then $k_1^2+k_2^2=$

If $(3+2 \sqrt{2})^{x^2-4}+(3-2 \sqrt{2})^{x^2-4}=6$, then $x^4+x^2+5=$

If -1 is a twice repeated root of the equation $a x^3+b x^2+c x+1=0$, then

If the equation $x^4+a x^3+b x^2+c x+d=0$ has three equal roots, then that root is

$\alpha$ and $\beta$ are the roots of the equation $x^2-a x+b=0$. If $\alpha^2+\beta^2$ and $\alpha^3+\beta^3$ are the roots of the equation $A x^2+B x+C=0$, then $C=$