For the system of linear equations

$$2x - y + 3z = 5$$

$$3x + 2y - z = 7$$

$$4x + 5y + \alpha z = \beta $$,

which of the following is NOT correct?

A line segment AB of length $$\lambda$$ moves such that the points A and B remain on the periphery of a circle of radius $$\lambda$$. Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius :

Let $$f$$ be a differentiable function such that $${x^2}f(x) - x = 4\int\limits_0^x {tf(t)dt} $$, $$f(1) = {2 \over 3}$$. Then $$18f(3)$$ is equal to :

Let the first term $$\alpha$$ and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to