Maths

Let $A=\left(\begin{array}{cc}\hfill 2\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 2\hfill \end{array}\right).$ If $B=I{-}^5\text{?}{C}_1\left(adjA\right){+}^5\text{?}{C}_2{\left(adjA\right)}^2-..{.}^5\text{?}{C}_5{\left(adjA\right)}^5,$ then the sum of all elements of the matrix B is

Let arg(z) represent the principal argument of the complex number z. Then $\left|z\right|=3$ and art(z – 1) – arg(z + 1) = $\frac{\pi }{4}$ intersect

Let α be root of the equation 1 + x² + x⁴ = 0. Then the value of α¹⁰¹¹ + α²⁰²² - α³⁰³³ is equal to

Let A = $\left\{Z\in C:\left|\frac{z+1}{z-1}\right|<1\right\}$and B = $\left\{z\in C:arg\left(\frac{z-1}{z+1}\right)=\frac{2\pi }{3}\right\}.$Then $A\cup B$ is

Let S = (0, 2) – $\left\{\frac{\pi }{2},\frac{3\pi }{4},\frac{3\pi }{2},\frac{7\pi }{4}\right\}.$ Let y = y(x), $x\in S,$ be the solution curve of the differential equation $\frac{dy}{dx}=\frac{1}{1+sin2x},y\left(\frac{\pi }{4}\right)=\frac{1}{2}.$ If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve $y=\sqrt[]{2}sinxis\frac{k\pi }{12},$ then k is equal to