For the following two (02) items:
Let $f(x) = a x ^ 2 + bx + c$ be a quadratic polynomial such that f(1) = f(4) = 2 Further, 2 is a root of f(x) = 0

What is (a + b + c) equal to?

For the following two (02) items:
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $

What is the value of the determinant of the matrix $A ^ 4$

For the following two (02) items:
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $

What is $[adj A ]^ {-1}$ equal to?

What is the sum of the binary numbers $(10110110) _2$ and $( 10001 1) _2$