A particle moving in the xy plane experiences a velocity dependent force
$$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$$ , where v_x and v_y are the
x and y components of its velocity $$\overrightarrow v $$ . If $$\overrightarrow a $$ is the
acceleration of the particle, then
which of the following statements is true for the particle?

The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is __________.

A Young's double-slit experiment is performed using monochromatic light of wavelength $$\lambda $$. The intensity of light at a point on the screen, where the path difference is $$\lambda $$, is K units. The intensity of light at a point where the path difference is $${\lambda \over 6}$$ is given by $${{nK} \over {12}}$$, where n is an integer. The value of n is __________.

The output characteristics of a transistor is shown in the figure.
When V_CE is 10V and I_C = 4.0 mA, then value of $$\beta $$_ac is __________.