Starting from $$\,{x_0} = 1,\,\,$$ one step of Newton - Raphson method in solving the equation $${x^3} + 3x - 7 = 0$$ gives the next value $${x_1}$$ as

Which of the following is a solution of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + \left( {q + 1} \right)y = 0?$$ Where $$p=4, q=3$$

The complete solution of the ordinary differential equation $${{{d^2}y} \over {d\,{x^2}}} + p{{dy} \over {dx}} + qy = 0$$ is $$\,y = {c_1}\,{e^{ - x}} + {C_2}\,{e^{ - 3x}}\,\,$$ then $$p$$ and $$q$$ are

Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method. The slope of the line is