The area enclosed by y² = 8x and y = $$\sqrt2$$ x that lies outside the triangle formed by y = $$\sqrt2$$ x, x = 1, y = 2$$\sqrt2$$, is equal to:

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 :