In a biprism experiment, monochromatic light of wavelength '$$\lambda$$' is used. The distance between two coherent sources '$$\mathrm{d}$$' is kept constant. If the distance between slit and eyepiece '$$\mathrm{D}$$' is varied as $$D_1, D_2, D_3 \& D_4$$ and corresponding measured fringe widths are $$Z_1, Z_2, Z_3$$ and $$Z_4$$ then

Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ each equal to $$2 \mathrm{a}$$. The mid points of $$A B$$ and $$A C$$ are $$D$$ and $$E$$ respectively. The work done in taking a charge $$Q$$ from $$D$$ to $$E$$ is ( $$\varepsilon_0=$$ permittivity of free space)

Light of frequency 1.5 times the threshold frequency is incident on photosensitive material. If the frequency is halved and intensity is doubled, the photocurrent becomes

A solid cylinder of mass $$3 \mathrm{~kg}$$ is rolling on a horizontal surface with velocity $$4 \mathrm{~m} / \mathrm{s}$$. It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is $$200 \mathrm{~N} / \mathrm{m}$$. The maximum compression produced in the spring will be (assume collision between cylinder & spring be elastic)