The sum $$\sum\limits_{k = 1}^{20} {k{1 \over {{2^k}}}} $$ is equal to

Which one of the following statements is not a tautology?

If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then the equation of the tangent to the hyperbola at (4,6) is :

If the system of linear equations

x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3

has a solution (x,y,z), z $$ \ne $$ 0, then (x,y) lies on the straight line whose equation is :