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 $$\Delta$$ $$\in$$ {$$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$} be such that (p $$\wedge$$ q) $$\Delta$$ ((p $$\vee$$ q) $$\Rightarrow$$ q) is a tautology. Then $$\Delta$$ 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 $$\cup$$ ..... $$\cup$$ Ak, where Ai $$\cap$$ Aj = $$\phi$$ for i $$\ne$$ j, 1 $$\le$$ j, j $$\le$$ k. Define the relation R from A to A by R = {(x, y) : y $$\in$$ Ai if and only if x $$\in$$ Ai, 1 $$\le$$ i $$\le$$ k}. Then, R is :