If the system of linear equations

2x + y $$-$$ z = 7

x $$-$$ 3y + 2z = 1

x + 4y + $$\delta$$z = k, where $$\delta$$, k $$\in$$ R has infinitely many solutions, then $$\delta$$ + k is equal to:

Let $$\alpha$$ and $$\beta$$ be the roots of the equation x² + (2i $$-$$ 1) = 0. Then, the value of |$$\alpha$$⁸ + $$\beta$$⁸| is equal to :

Let $$A = [{a_{ij}}]$$ be a square matrix of order 3 such that $${a_{ij}} = {2^{j - i}}$$, for all i, j = 1, 2, 3. Then, the matrix A² + A³ + ...... + A¹⁰ is equal to :

Let a set A = A₁ $$\cup$$ A₂ $$\cup$$ ..... $$\cup$$ A_k, where A_i $$\cap$$ A_j = $$\phi$$ for i $$\ne$$ j, 1 $$\le$$ j, j $$\le$$ k. Define the relation R from A to A by R = {(x, y) : y $$\in$$ A_i if and only if x $$\in$$ A_i, 1 $$\le$$ i $$\le$$ k}. Then, R is :