The area enclosed by the curves $${y^2} + 4x = 4$$ and $$y - 2x = 2$$ is :

The equation $${x^2} - 4x + [x] + 3 = x[x]$$, where $$[x]$$ denotes the greatest integer function, has :

If A and B are two non-zero n $$\times$$ n matrices such that $$\mathrm{A^2+B=A^2B}$$, then :

For three positive integers p, q, r, $${x^{p{q^2}}} = {y^{qr}} = {z^{{p^2}r}}$$ and r = pq + 1 such that 3, 3 log$$_yx$$, 3 log$$_zy$$, 7 log$$_xz$$ are in A.P. with common difference $$\frac{1}{2}$$. Then r-p-q is equal to