The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x $$-$$ y + 4z = 8

A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :

If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)²⁰²² is divided by 8 is __________.

The total number of two digit numbers 'n', such that 3ⁿ + 7ⁿ is a multiple of 10, is __________.